8512
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 28
- Divisor Sum
- 20320
- Proper Divisor Sum (Aliquot Sum)
- 11808
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3456
- Möbius Function
- 0
- Radical
- 266
- Omega Function (Ω)
- 8
- 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
- 34
- 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
- Restricted partitions.at n=14A001981
- Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid.at n=4A007764
- Number of nonintersecting rook paths joining opposite corners of 5 X n board.at n=4A007787
- Expansion of e.g.f. sinh(tan(x)*exp(x)).at n=7A009608
- sec(cos(x)-cosh(x)) = 1+12/4!*x^4+8512/8!*x^8+41692992/12!*x^12...at n=2A013480
- E.g.f. exp(sec(x)-sech(x)) (even powers only).at n=4A013503
- cosh(sec(x)-sech(x)) = 1+12/4!*x^4+8512/8!*x^8+34406592/12!*x^12...at n=2A013513
- First row of spectral array W(sqrt(3)).at n=21A022159
- a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3).at n=41A024312
- a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor( n/2 ), s = natural numbers >= 3.at n=40A024875
- a(n) = d(n)/2, where d = A026040.at n=34A026041
- 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 45.at n=30A031543
- Numbers k such that 81*2^k+1 is prime.at n=50A032390
- Total number of prime parts in all partitions of n.at n=25A037032
- Number of ways n*(n-1) can be partitioned into the sum of 2*(n-1) integers in the range 0..n.at n=8A039744
- Denominators of continued fraction convergents to sqrt(139).at n=9A041255
- Digits d in decimal expansion of n replaced with d^3.at n=28A048390
- Numbers n such that x^n + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).at n=46A057484
- Numbers k such that sigma(x) = k has exactly 7 solutions.at n=34A060663
- Numbers n such that n | p(n)*q(n), where p() is the unrestricted partition function (A000041) and q is the distinct partition function (A000009).at n=47A060744