13170
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
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 31680
- Proper Divisor Sum (Aliquot Sum)
- 18510
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3504
- Möbius Function
- 1
- Radical
- 13170
- Omega Function (Ω)
- 4
- Little Omega Function (ω)
- 4
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
- 138
- 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
- yes
- Odd
- no
Appears in sequences
- Exponential self-convolution of numbers of trees on n nodes.at n=10A006771
- T(2n+6,n), array T as in A055216.at n=6A055222
- Number of primitive (aperiodic) step shifted (decimated) sequences using a maximum of five different symbols.at n=6A056384
- Triangle T(n,k) of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes and with k edges, k=0..binomial(n+1,2).at n=48A060517
- a(n) = floor((-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1))) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.at n=17A065955
- Sum of the first moments of all partitions of n with weights starting at 0.at n=18A066185
- Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 0), (-1, 1, 1), (1, 0, -1), (1, 0, 1)}.at n=8A149312
- a(n) = (3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30.at n=13A161704
- Number of increasing sequences of n integers x(1),...,x(n) with values in 1..5*n such that x(j) divides x(k) iff j divides k.at n=20A180382
- Number of n X 6 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.at n=3A232333
- T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.at n=39A232335
- Number of 4Xn 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.at n=5A232338
- Number of (n+2)X(1+2) 0..3 arrays with no row, column, diagonal or antidiagonal in any 3X3 subblock summing to 0 1 2 7 8 or 9.at n=0A252587
- T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no row, column, diagonal or antidiagonal in any 3X3 subblock summing to 0 1 2 7 8 or 9.at n=0A252590
- Number of (n+2)X(4+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101.at n=6A260837
- Number of (n+2)X(7+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101.at n=3A260840
- Triangle read by rows: T(n,k) is the coefficient of (1+x)^k in the ZZ polynomial of the hexagonal graphene flake O(3,3,n).at n=54A338217
- Square array A(n, k) = A294898(A246278(n, k)), read by falling antidiagonals; Difference A005187(n)-A000203(n) applied to the prime shift array.at n=70A379008