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A328851 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k + 1). 3

%I #12 Nov 15 2021 12:35:34

%S 1,3,4,11,6,19,8,34,20,29,12,78,14,39,40,104,18,107,20,120,54,59,24,

%T 277,47,69,88,162,30,237,32,299,82,89,84,478,38,99,96,429,42,321,44,

%U 246,230,119,48,921,86,258,124,288,54,535,128,581,138,149,60,1091

%N Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k + 1).

%C Number of ways to factor n into 3 kinds of 2, 4 kinds of 3, ..., k+1 kinds of k.

%C Dirichlet convolution of A001055 with A050367.

%H Antti Karttunen, <a href="/A328851/b328851.txt">Table of n, a(n) for n = 1..4096</a>

%F a(n) = Sum_{d|n} A001055(n/d) * A050367(d).

%o (PARI) seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n,k), p=1/(1 - x + O(x*x^m))^(1+k), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p,i)); v=dirmul(v,w)); v} \\ _Andrew Howroyd_, Oct 28 2019

%Y Cf. A001055, A050367, A328853.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Oct 28 2019

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Last modified June 19 18:58 EDT 2024. Contains 373507 sequences. (Running on oeis4.)