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%I #5 Oct 11 2017 18:10:00
%S 1,0,1,1,2,2,5,4,8,9,15,16,28,29,46,54,77,90,131,150,211,251,337,401,
%T 540,637,839,1006,1296,1551,1995,2373,3013,3610,4523,5410,6754,8045,
%U 9965,11897,14614,17410,21313,25316,30816,36615,44307,52539,63387,74975,90078
%N Expansion of Product_{k>=2} 1/(1 - x^k)^omega(k), where omega(k) is the number of distinct primes dividing k (A001221).
%C Euler transform of A001221.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: Product_{k>=2} 1/(1 - x^k)^b(k), where b(k) = [x^k] Sum_{j>=1} x^prime(j)/(1 - x^prime(j)).
%F a(0) = 1; a(n) = (1/n)*Sum_{k=1..n} a(n-k)*b(k), b(k) = Sum_{d|k} d*omega(d).
%t nmax = 50; CoefficientList[Series[Product[1/(1 - x^k)^PrimeNu[k], {k, 2, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d PrimeNu[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 50}]
%Y Cf. A001221, A006171, A293549.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Oct 11 2017
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