13137
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 15
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 18240
- Proper Divisor Sum (Aliquot Sum)
- 5103
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 8400
- Möbius Function
- -1
- Radical
- 13137
- 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
- 213
- 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
- Glaisher's function H'(4n+1) (18 squares version).at n=29A002610
- a(n) = floor((Pi/2)^n).at n=21A014214
- Denominators of continued fraction convergents to sqrt(976).at n=9A042889
- Number of 3 X 3 integer matrices with elements in the range [ -n,n ] which represent a rotation of order 2.at n=9A053171
- G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(4n))...)^12)^8)^4.at n=5A138214
- Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 1), (0, 1), (1, -1), (1, 1)}.at n=10A151417
- Decimal representation of the middle column of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.at n=13A265700
- p*B_(p-1)+1 modulo p^2, where p = prime(n) and B_i denotes the i-th Bernoulli number.at n=35A268000
- a(n) = (n-1)! + 1 mod n^3.at n=28A301317
- a(n) = Sum_{k=1..n} k * tau_3(k), where tau_3 is A007425.at n=44A318750
- a(n) is the smallest number that is the sum of n positive 6th powers in two ways.at n=30A343079
- Numbers k such that A361338(k) = 8.at n=51A361347
- Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x) ).at n=4A377832