A050369 Number of ordered factorizations of n into 2 kinds of 2, 3 kinds of 3, ...
1, 2, 3, 8, 5, 18, 7, 32, 18, 30, 11, 96, 13, 42, 45, 128, 17, 144, 19, 160, 63, 66, 23, 480, 50, 78, 108, 224, 29, 390, 31, 512, 99, 102, 105, 936, 37, 114, 117, 800, 41, 546, 43, 352, 360, 138, 47, 2304, 98, 400, 153, 416, 53, 1080, 165, 1120, 171, 174, 59, 2640
Offset: 1
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A074206.
Programs
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Mathematica
a[1]=1; a[n_]:=a[n]=n*Sum[If[d==n,0,a[d]/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}] (* Vaclav Kotesovec, Feb 02 2019 *)
Formula
Dirichlet g.f.: 1/(2-zeta(s-1)).
a(n) = n*Sum_{d divides n, d1, a(1)=1. - Vladeta Jovovic, Feb 09 2002
Sum_{k=1..n} a(k) ~ -n^(1+r) / ((1+r)*Zeta'(r)), where r = A107311 = 1.728647238998183618135103010297... is the root of the equation Zeta(r) = 2. - Vaclav Kotesovec, Feb 02 2019
G.f. A(x) satisfies: A(x) = x + 2*A(x^2) + 3*A(x^3) + 4*A(x^4) + ... - Ilya Gutkovskiy, May 10 2019
For n > 0, a(n) = n * A074206(n). - Vaclav Kotesovec, Mar 18 2021
Comments