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%I #7 Oct 29 2019 12:15:13
%S 1,3,4,8,6,19,8,25,16,29,12,66,14,39,40,69,18,95,20,102,54,59,24,220,
%T 41,69,72,138,30,237,32,191,82,89,84,379,38,99,96,342,42,321,44,210,
%U 206,119,48,679,78,240,124,246,54,459,128,464,138,149,60,971
%N Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(k + 1).
%C Number of ways to factor n into distinct factors with 3 kinds of 2, 4 kinds of 3, ..., k+1 kinds of k.
%C Dirichlet convolution of A045778 with A050368.
%F a(n) = Sum_{d|n} A045778(n/d) * A050368(d).
%o (PARI) seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n, k), p=(1 + x + O(x*x^m))^(k+1), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w)); v} \\ _Andrew Howroyd_, Oct 29 2019
%Y Cf. A045778, A050368, A328851, A328877.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Oct 29 2019