13700
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 18
- Divisor Sum
- 29946
- Proper Divisor Sum (Aliquot Sum)
- 16246
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 5440
- Möbius Function
- 0
- Radical
- 1370
- Omega Function (Ω)
- 5
- 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
- 58
- 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
- Total number of ordered k-tuples (k=0..n) of distinct elements from an n-element set: a(n) = Sum_{k=0..n} n!/k!.at n=7A000522
- Number of inequivalent ways to color vertices of a regular tetrahedron using <= n colors.at n=20A006008
- Expansion of 1/Product_{m>=1} (1 - m*q^m)^2.at n=11A022726
- a(n) = n*(n^2 + 12*n - 25)/6.at n=40A026057
- a(n) = A027082(n, n+3).at n=11A027085
- Numbers k such that 105*2^k+1 is prime.at n=39A032402
- Numbers k such that k^128 + 1 is prime.at n=37A056994
- Triangle T(n,k) read by rows, where e.g.f. for T(n,k) is exp((1+y)*x)/(1-x).at n=28A073107
- Triangle T(n,k) read by rows, where o.g.f. for T(n,k) is n!*Sum_{k=0..n} (1+x)^(n-k)/k!.at n=28A073474
- Binomial triangle based on factorials.at n=35A076571
- Expansion of (1-x)/(1-x-2*x^2-2*x^3).at n=13A078006
- Square array of numbers related to the incomplete gamma function, read by antidiagonals.at n=43A080955
- Transposed version of A080955: T(n,k) = A080955(k,n), n>=0, k>=-1.at n=52A089258
- Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having along the lower contour exactly k reentrant corners, i.e., a vertical step that is followed by a horizontal step (n>=1, k>=0).at n=16A121579
- Triangle read by rows: T(n,k) is the number of deco polyominoes of height n such that the bottom of the last column is at level k (n>=1; k>=0). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.at n=22A121632
- Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and such that the sum of the bottom levels of all columns is k (n>=1, k>=0; informally, the number of the "missing" cells in the right bottom corner of the polyomino). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.at n=29A122104
- Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} in which the last entry of the first increasing run is equal to k (1 <= k <= n).at n=35A134433
- Array read by antidiagonals, a(n,k) = gamma(n+1,k)*e^k, where gamma(n,k) is the upper incomplete gamma function and e is the exponential constant 2.71828...at n=37A134558
- Square array read by antidiagonals: form the Euler-Seidel matrix for the sequence {k!} and then divide column k by k!.at n=28A143409
- Square array read by antidiagonals upwards: T(n,k) is the number of scenarios for the gift exchange problem in which each gift can be stolen at most once, when there are n gifts in the pool and k gifts (not yet frozen) in peoples' hands.at n=43A144502