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

1,2

Comments

Dirichlet inverse of (A000027*A153881). - Mats Granvik, Jan 03 2009

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

Dirichlet g.f.: 1/(2-zeta(s-1)).

a(n) = n*Sum_{d divides n, d<n} a(d)/d, n>1, 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

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 *)

Crossrefs

Cf. A074206.

Sequence in context: A004730 A332460 A168014 * A070935 A095164 A075384

Adjacent sequences: A050366 A050367 A050368 * A050370 A050371 A050372

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved