AI & ChatGPT searches , social queries for CENTERED ICOSAHEDRAL-NUMBER
Search references for CENTERED ICOSAHEDRAL-NUMBER. Phrases containing CENTERED ICOSAHEDRAL-NUMBER
See searches and references containing CENTERED ICOSAHEDRAL-NUMBER!
Search references for CENTERED ICOSAHEDRAL-NUMBER. Phrases containing CENTERED ICOSAHEDRAL-NUMBER
See searches and references containing CENTERED ICOSAHEDRAL-NUMBER!CENTERED ICOSAHEDRAL-NUMBER
Three-dimensional figurate centered icosahedral numbers
of a cuboctahedron, and are a magic number for the face-centered cubic lattice. The centered icosahedral number for a specific n {\displaystyle n} is
Centered_icosahedral_number
Figurate number representing an icosahedron
In mathematics, an icosahedral number is a figurate number that represents an icosahedron. The nth icosahedral number is given by the formula n ( 5 n 2
Icosahedral_number
Natural number
integer and a centered icosahedral number. 310 = 2 × 5 × 31. It is a sphenic number meaning that it has 3 prime factors. It is a noncototient number because
300_(number)
Natural number
[and] forty-seven) is the natural number following 146 and preceding 148. 147 is the fourth centered icosahedral number. These are a class of figurate numbers
147_(number)
Number that represents a hexagon with a dot in the center
combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the center and all
Centered_hexagonal_number
Type of figurate number
additional layer. Centered tetrahedral numbers Centered cube numbers Centered octahedral numbers Centered dodecahedral numbers Centered icosahedral numbers Stella
Centered_polyhedral_number
Number used for counting
natural-number results: subtracting a larger natural number from a smaller one results in a negative number and dividing one natural number by another
Natural_number
Class of series of figurate numbers, each having a central dot
nth centered k-gonal number can be obtained by placing k copies of the (n−1)th triangular number around a central point; therefore, the nth centered k-gonal
Centered_polygonal_number
Number divisible only by 1 and itself
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that
Prime_number
Regular tiling of hyperbolic 3-space
In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli
Icosahedral_honeycomb
Number of dots in a centred dot square
elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all
Centered_square_number
Figurate number
Knowing the triangular numbers, one can reckon any centered polygonal number; the nth centered k-gonal number is obtained by the formula C k n = k T n − 1 +
Triangular_number
Integer having a non-trivial divisor
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has
Composite_number
3D symmetry group
an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include
Icosahedral_symmetry
Number equal to the sum of its proper divisors
hexagonal number. Furthermore, each even perfect number except for 6 is the 2 p + 1 3 {\displaystyle {\tfrac {2^{p}+1}{3}}} -th centered nonagonal number and
Perfect_number
Centered figurate number that represents a pentagon with a dot in the center
In mathematics, a centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding
Centered_pentagonal_number
Centered figurate number that represents a triangle with a dot in the center
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other
Centered_triangular_number
Type of figurate number
both hexagonal and perfect squares starts 1, 1225, 1413721,... OEIS: A046177. Centered hexagonal number Weisstein, Eric W. "Hexagonal Number". MathWorld.
Hexagonal_number
Numbers obtained by adding the two previous ones
month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive
Fibonacci_sequence
Natural number
5th triangular number, a hexagonal number, and pentadecagonal number. It is also a centered tetrahedral number. 15 is a lucky number. 15 is the smallest
15_(number)
Number that when multiplied by another number moves its last digit to its front
In mathematics, an n-parasitic number (in base 10) is a positive natural number which, when multiplied by n, results in movement of the last digit of its
Parasitic_number
Product of an integer with itself
Every odd square is also a centered octagonal number. Another property of a square number is that (except 0) it has an odd number of positive divisors, while
Square_number
Recursive integer sequence
they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients
Catalan_number
Centered figurate number that represents a nonagon with a dot in the center
A centered nonagonal number, (or centered enneagonal number), is a centered figurate number that represents a nonagon with a dot in the center and all
Centered_nonagonal_number
Figurate number
numbers are closely related to centered hexagonal numbers. When the array corresponding to a centered hexagonal number is divided between its middle row
Pentagonal_number
Number used to approximate the square root of 2
starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the
Pell_number
Number that remains the same when its digits are reversed
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are
Palindromic_number
Numbers with a certain property involving recursive summation
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance
Happy_number
Number that is less than the sum of its proper divisors
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The
Abundant_number
Centered figurate number that counts points in a three-dimensional pattern
is the number of points in a body-centered cubic pattern within a cube that has n + 1 points along each of its edges. The first few centered cube numbers
Centered_cube_number
Prime number of the form 2^n – 1
mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer
Mersenne_prime
Composite number in number theory
In number theory, a Carmichael number is a composite number n {\displaystyle n} which in modular arithmetic satisfies the congruence relation: b n
Carmichael_number
Integer divisible by sum of its digits
In recreational mathematics, a Harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written
Harshad_number
Honeycomb made from unique polyhedrons
In the geometry of hyperbolic 3-space, the dodecahedral-icosahedral honeycomb is a uniform honeycomb, constructed from dodecahedron, icosahedron, and
Dodecahedral-icosahedral honeycomb
Dodecahedral-icosahedral_honeycomb
Centered figurate number that represents a decagon with a dot in the center
centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot
Centered_decagonal_number
Centered figurate number that represents a heptagon with a dot in the center
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center
Centered_heptagonal_number
Natural number
primes is divisible by 455. 456 = 23 × 3 × 19. It is a centered pentagonal number, an icosahedral number, the sum of a pair of twin primes (227 + 229), and
400_(number)
Odd number with specific properties
In number theory, a Sierpiński number is an odd natural number k such that k × 2 n + 1 {\displaystyle k\times 2^{n}+1} is composite for all natural numbers
Sierpiński_number
Centered figurate number representing an octahedron
In mathematics, a centered octahedral number or Haüy octahedral number is a figurate number that counts the points of a three-dimensional integer lattice
Centered_octahedral_number
Centered figurate number that represents an octagon with a dot in the center
centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center
Centered_octagonal_number
Integer whose multiples are digit rotations
number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely-known cyclic number is
Cyclic_number
Solid with twenty equal triangular faces
vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra
Regular_icosahedron
Type of composite number with an even number of digits
recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into
Vampire_number
Infinite integer series where the next number is the sum of the two preceding it
numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47
Lucas_number
Area of a right triangle with rational-numbered sides
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition
Congruent_number
Number whose square ends in the same digits
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose
Automorphic_number
Number of form 2^(2^p-1)-1 with prime exponent
In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p {\displaystyle
Double_Mersenne_number
Natural number
number and the 38th triangular number. 742 = 2 × 7 × 53. It is a sphenic number, a decagonal number, an icosahedral number, and a lazy caterer number
700_(number)
Integer having only small prime factors
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is
Smooth_number
Centered figurate number representing a dodecahedron
mathematics, a centered dodecahedral number is a centered figurate number that represents a dodecahedron. The centered dodecahedral number for a specific
Centered_dodecahedral_number
Integer whose representation contains every digit in its number base
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For
Pandigital_number
Base-dependent property of integers
In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can
Kaprekar_number
Positive integer of the form (2^(2^n))+1
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: F n
Fermat_number
Concept in number theory
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus
Narcissistic_number
Iterative algorithm on numbers
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with
Kaprekar's_routine
Ordered chemical structure with no repeating pattern
a local icosahedral order. The icosahedral order is in equilibrium in the liquid state for the stable quasicrystals, whereas the icosahedral order prevails
Quasicrystal
Product of two prime numbers
In number theory, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other
Semiprime
Number, non-palindrome after repeated sum with reverse
numbers exist? More unsolved problems in mathematics A Lychrel number is a natural number that cannot form a palindrome through the iterative process of
Lychrel_number
Square of a triangular number
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2
Squared_triangular_number
Type of number introduced by Mike Keith
mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n {\displaystyle n} in a given number base b {\displaystyle
Keith_number
Type of figurate number
The number 1225 is hecatonicositetragonal (s = 124), hexacontagonal (s = 60), icosienneagonal (s = 29), hexagonal, square, and triangular. Centered polygonal
Polygonal_number
Mathematical sequences in combinatorics
frequently arise in combinatorics. Moreover, all three can be defined as the number of partitions of n elements into k non-empty subsets, where each subset
Stirling_number
Polyhedral number representing a tetrahedron
n is the number of houses. Centered triangular number Simplex number http://demonstrations.wolfram.com/GeometricProofOfTheTetrahedralNumberFormula Baumann
Tetrahedral_number
Two or more natural numbers with a common abundancy index
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and
Friendly_number
Numbers with many divisors
highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive
Highly_composite_number
Natural number between 89 and 91
triangular number 78 is the only number to have an aliquot sum equal to 90, aside from the square of the twenty-fourth prime, 892 (which is centered octagonal)
90_(number)
Centered figurate number
also called centered dodecagonal numbers because star numbers are centered polygonal numbers with a twelve-sided shape. The nth star number is given by
Star_number
Number of points in an octagonal arrangement
more commonly used to refer to centered dodecagonal numbers. The n {\displaystyle n} th octagonal number is the number of partitions of 6 n − 5 {\displaystyle
Octagonal_number
Number whose sums of distinct divisors represent all smaller numbers
In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented
Practical_number
Number equal to the sum of all or some of its divisors
In number theory, a semiperfect number or pseudoperfect number is a natural number n equal to the sum of all or some of its proper divisors. A semiperfect
Semiperfect_number
Type of Poulet number
In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle
Super-Poulet_number
Figurate number
A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers,
Pyramidal_number
Size of a geometric arrangement of points
= 82. There is a similar gnomon with centered hexagonal numbers adding up to make cubes of each integer number. Dickson, L. E. (1919), History of the
Figurate_number
Integer filtered out using a sieve similar to that of Eratosthenes
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes
Lucky_number
Positive integer whose divisors have a harmonic mean that is an integer
In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic
Harmonic_divisor_number
Number raised to the third power
curve has a center of symmetry at the origin, but no axis of symmetry. A cube number, or a perfect cube, or sometimes just a cube, is a number which is the
Cube_(algebra)
Mathematical concept
Cullen number is a member of the integer sequence C n = n ⋅ 2 n + 1 {\displaystyle C_{n}=n\cdot 2^{n}+1} (where n {\displaystyle n} is a natural number). Cullen
Cullen_number
Number that is the result of operation on its own digits
A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination
Friedman_number
Mathematical concept in prime numbers
power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing
Idoneal_number
Conjectures in additive number theory
confirmed true in 2025. Pollock centered nonagonal numbers conjecture: Every positive integer is the sum of at most 11 centered nonagonal numbers. This conjecture
Pollock's_conjectures
Count of the possible partitions of a set
2,5,15,52,203,877,4140,\dots } (sequence A000110 in the OEIS). The Bell number B n {\displaystyle B_{n}} counts the different ways to partition a set that
Bell_number
Number of stacked spheres in a pyramid
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The
Square_pyramidal_number
Triangular array of natural numbers
numbers N ( n , k ) {\displaystyle \operatorname {N} (n,k)} , is the number of words containing n {\displaystyle n} pairs of parentheses, which
Narayana_number
Ten raised to an integer power
the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one
Power_of_10
Numbers whose sum of divisors is twice the number plus 1
unsolved problems in mathematics In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function
Quasiperfect_number
Arithmetic operation
give the number of possible values for an n-bit integer binary number; for example, a byte may take 28 = 256 different values. The binary number system
Exponentiation
Archimedean solid with 62 faces
J. V. Field, 1997, ISBN 0-87169-209-0 (page 123) Weisstein, Eric W. "Icosahedral group". MathWorld. Weisstein, Eric W. "Zome". MathWorld. Read, R. C.;
Rhombicosidodecahedron
Type of composite integer
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its
Smith_number
Polyhedron made from triangles that approximates a sphere
polyhedron made from triangles which approximates a sphere. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices
Geodesic_polyhedron
Number, product of consecutive integers
The nth pronic number is also the difference between the odd square (2n + 1)2 and the (n+1)st centered hexagonal number. Since the number of off-diagonal
Pronic_number
Class of natural numbers with many divisors
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is
Superior highly composite number
Superior_highly_composite_number
Positive integer with large prime factors
A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately
Rough_number
Property of a number
In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point at which
Persistence_of_a_number
Number whose divisors add to a multiple of that number
perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is
Multiply_perfect_number
Two raised to an integer power
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with the number two as the base and integer n as
Power_of_two
Integer of the form 3 × 2^n – 1 for non-negative n
In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 ⋅ 2 n − 1 {\displaystyle 3\cdot 2^{n}-1} for a non-negative
Thabit_number
Number of close-packed spheres in an octahedron
quadratae secundae". The number of cubes in an octahedron formed by stacking centered squares is a centered octahedral number, the sum of two consecutive
Octahedral_number
Numbers parameterizing ways to partition a set
particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Numbers that evenly divide powers of 60
length be a regular number. Book VIII of Plato's Republic involves an allegory of marriage centered on the highly regular number 604 = 12,960,000 and
Regular_number
Type of natural number
In number theory, a self number in a given number base b {\displaystyle b} is a natural number that cannot be written as the sum of any other natural
Self_number
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER
CENTERED ICOSAHEDRAL-NUMBER