13409
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 17
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 15552
- Proper Divisor Sum (Aliquot Sum)
- 2143
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 11440
- Möbius Function
- -1
- Radical
- 13409
- 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
- 120
- 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
- Expansion of e.g.f.: exp(sinh(sin(x))).at n=10A009219
- Number of partitions satisfying (cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5) and cn(4,5) <= cn(2,5) and cn(4,5) <= cn(3,5)).at n=45A036803
- Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= n/3.at n=33A048002
- Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= (n-1)/3.at n=33A048015
- Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= (n+1)/3.at n=33A048048
- Numbers k such that gcd(3k,8^k+1) = 3 but k does not divide the numerator of B(2k) (the Bernoulli numbers).at n=19A070193
- a(1)=1, a(n+1) = a(n) + spf(Sum_{i=1..n} a(i)), where spf=A020639 (smallest prime factor).at n=26A080180
- Numbers k such that k + sigma(k) + phi(k) is a square.at n=21A116009
- a(n) = 104*n + 9977.at n=33A126978
- a(n) = (2*n^3 + 5*n^2 - 7*n)/2.at n=22A162261
- Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| != w+x+y.at n=23A213485
- Number of partitions p of n such that #m(1) = #m(2), where #m(i) = number of numbers in p that have multiplicity i.at n=46A241518
- a(n) = A266196(A000079(n)); indices of powers of 2 in A266195.at n=29A266186
- Smallest number such that the sum of the digits of n * a(n) is greater than n.at n=43A269333
- Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 105", based on the 5-celled von Neumann neighborhood.at n=26A285827
- One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 4 mod 7 (except for the initial 0).at n=5A290809
- Expansion of 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^(k*(k+1)*(k+2)/6)/(1 - ...))))))), a continued fraction.at n=32A295072
- a(n) = n*(n + 1)*(7*n + 5)/6.at n=22A304993
- a(n) = Sum_{d|n} mu(n/d) * binomial(d,3).at n=45A346760
- Positive integers in which the sum of the k-th powers of their digits is a prime number for k = 1, 2, 3, 4, 5, and 6 but not for k=7.at n=44A359449