12585
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 21
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 20160
- Proper Divisor Sum (Aliquot Sum)
- 7575
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6704
- Möbius Function
- -1
- Radical
- 12585
- Omega Function (Ω)
- 3
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 107
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- yes
- 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
- no
- Odd
- yes
Appears in sequences
- McKay-Thompson series of class 14B for Monster.at n=32A058503
- Number of partitions of n with parts occurring at most thrice and an odd number of parts. Row sums of A098490.at n=45A098492
- G.f. A(x) satisfies: A(x) = P(x*A(x)) where P(x) = A(x/P(x)) is the g.f. of the partition numbers A000041.at n=8A109085
- McKay-Thompson series of class 28B for the Monster group.at n=32A112169
- a(1) = 1; for n > 1, a(n) = (2^n-1)*a(n-1) + (-1)^n.at n=4A123672
- a(n) = Sum_{k=0..n} 2^(n-k)*C(2n,n-k).at n=5A128418
- Expansion of q^-1 * (chi(-q) * chi(-q^7))^3 in powers of q where chi() is a Ramanujan theta function.at n=32A132319
- Divisors of 453060.at n=33A134950
- a(n) = 839*n.at n=15A135639
- Numbers k such that k and k^2 use only the digits 1, 2, 3, 5 and 8.at n=23A136976
- a(n) = 484*n + 1.at n=25A158326
- a(n) = 26*n^2 + 1.at n=22A158549
- Number of binary strings of length n with equal numbers of 0000 and 0010 substrings.at n=15A164148
- a(n) = A030068(4n+1).at n=43A169739
- Triangular array: the fission of ((2x+1)^n) by (q(n,x)), where q(n,x)=x^n+x^(n-1)+...+x+1.at n=50A193860
- Mirror of the triangle A193860.at n=49A193861
- Number of 0..n arrays x(0..10) of 11 elements with zero 6th differences.at n=29A200447
- Number of partitions of n into exactly 7 different parts with distinct multiplicities.at n=17A212118
- Number of partitions p of n such that (number of even numbers in p) >= 2*(number of odd numbers in p).at n=45A241644
- Expansion of -(2*x*sqrt(1-8*x^2)-2*x) / (16*x^3+sqrt(1-8*x^2)*(4*x^2+2*x-1)-8*x^2-2*x+1).at n=10A243019