13521
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 18032
- Proper Divisor Sum (Aliquot Sum)
- 4511
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 9012
- Möbius Function
- 1
- Radical
- 13521
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
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
- 89
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- 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
- Number of partitions of n with zero crank.at n=52A064410
- Number of terms of A100873 less than 10^n.at n=11A100874
- Sum of all terms on the two principal diagonals of a 2n+1 X 2n+1 square spiral.at n=13A114254
- The sum of the principal diagonals of an n X n spiral.at n=27A137930
- a(n) = Sum_{k=0..n} ( Fibonacci(2*k-1) + (n-k)*Fibonacci(2*k) ).at n=10A141752
- Number of planar n X n X n binary triangular grids symmetric under 120 degree rotation with no more than 4 ones in any 3 X 3 X 3 subtriangle.at n=9A153929
- a(n) = 338*n + 1.at n=39A158000
- a(n) = 676*n + 1.at n=19A158386
- a(n) = 20*n^2 + 1.at n=26A158493
- a(n) = 80*n^2 + 1.at n=13A158776
- E.g.f. A(x) satisfies A(x)=exp(x*A(x))*(1+x*A(x))/(1-x*A(x)-x^2*A(x)^2).at n=4A186451
- Constant term of the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.at n=8A192376
- Semiprimes of the form 5*n^2 + 1.at n=15A212707
- a(n) = (n^4 - n^3 + 4*n^2 + 2)/2.at n=13A239592
- Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 0,-1 -2,0 or 1,1.at n=10A264874
- Numbers k such that (266*10^k - 17)/3 is prime.at n=25A273944
- Expansion of Product_{k>=1} (1 + x^k)^prime(k+1).at n=11A353169
- Number of multiset partitions of integer partitions of n such that all blocks are gapless.at n=16A356941
- G.f.: Sum_{k>=0} x^k * Product_{j=1..4*k} (1 + x^j)/(1 - x^j).at n=20A385090