12672
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 4
Divisibility
- Divisor Count
- 48
- Divisor Sum
- 39780
- Proper Divisor Sum (Aliquot Sum)
- 27108
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3840
- Möbius Function
- 0
- Radical
- 66
- Omega Function (Ω)
- 10
- Little Omega Function (ω)
- 3
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- yes
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 32
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Appears in sequences
- E.g.f. sin(sinh(x)) (odd powers only).at n=5A003722
- Number of non-vanishing Feynman diagrams of order 2n+1 for the electron-electron-photon proper vertex function in quantum electrodynamics (QED).at n=5A005413
- Theta series of {D_9}* lattice.at n=28A008424
- Number of ways of writing n as a sum of 9 squares.at n=7A008452
- Theta series of direct sum of 2 copies of f.c.c. lattice.at n=23A008663
- Expansion of e.g.f. cos(sinh(x))/exp(x).at n=10A009059
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (odd natural numbers), t = A000201 (lower Wythoff sequence).at n=35A024599
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (odd natural numbers), t = A000201 (lower Wythoff sequence).at n=34A025113
- Numbers that are the sum of 4 nonzero squares in exactly 10 ways.at n=44A025366
- a(n) = n + (n+1)^2 + (n+2)^3.at n=21A027620
- Expansion of (theta_3(z^4)^3 + theta_2(z^4)^3)^3.at n=28A028696
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 55.at n=34A031553
- Number of increasing asymmetric rooted connected graphs where every block is a complete graph.at n=7A035081
- Smallest natural number k such that periodic part of 1/k is n, or 0 if no such k exists.at n=41A037207
- Smallest natural number k such that periodic part of 1/k is n, or 0 if no such k exists.at n=14A037207
- Smallest natural number k such that periodic part of 1/k is the prime p(n), or 0 if no such k exists.at n=12A037218
- Number of 2n-bead balanced binary necklaces of fundamental period 2n which are equivalent to their reverse, but not equivalent to their complement and reversed complement.at n=16A045685
- Number of nonnegative solutions of x1^2 + x2^2 + ... + x9^2 = n.at n=26A045851
- Numbers that are divisible by exactly 10 primes with multiplicity.at n=26A046314
- a(n) = (1/24)*n*(n + 5)*(n^2 + n + 6).at n=21A051743