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%I #24 Mar 18 2021 09:07:48
%S 1,2,3,8,5,18,7,32,18,30,11,96,13,42,45,128,17,144,19,160,63,66,23,
%T 480,50,78,108,224,29,390,31,512,99,102,105,936,37,114,117,800,41,546,
%U 43,352,360,138,47,2304,98,400,153,416,53,1080,165,1120,171,174,59,2640
%N Number of ordered factorizations of n into 2 kinds of 2, 3 kinds of 3, ...
%C Dirichlet inverse of (A000027*A153881). - _Mats Granvik_, Jan 03 2009
%H Vaclav Kotesovec, <a href="/A050369/b050369.txt">Table of n, a(n) for n = 1..10000</a>
%F Dirichlet g.f.: 1/(2-zeta(s-1)).
%F a(n) = n*Sum_{d divides n, d<n} a(d)/d, n>1, a(1)=1. - _Vladeta Jovovic_, Feb 09 2002
%F 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
%F 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
%F For n > 0, a(n) = n * A074206(n). - _Vaclav Kotesovec_, Mar 18 2021
%t 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 *)
%Y Cf. A074206.
%K nonn
%O 1,2
%A _Christian G. Bower_, Oct 15 1999
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