A327725 - OEIS

%I #9 Sep 23 2019 14:03:33

%S 1,0,1,1,1,2,3,3,4,6,7,9,12,14,18,24,27,35,43,51,64,79,92,113,137,162,

%T 195,235,276,329,394,460,546,646,753,890,1044,1214,1422,1662,1927,

%U 2245,2611,3015,3497,4051,4662,5385,6209,7128,8203,9423,10786

%N Expansion of Product_{i>=1, j>=1}  (1 + x^(i*prime(j))).

%C Weigh transform of A001221.

%F G.f.: Product_{k>=1} (1 + x^k)^A001221(k).

%t nmax = 52; CoefficientList[Series[Product[(1 + x^k)^PrimeNu[k], {k, 1, nmax}], {x, 0, nmax}], x]

%t a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d PrimeNu[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}]

%o (PARI) seq(n)={Vec(prod(k=1, n, (1 + x^k + O(x*x^n))^omega(k)))} \\ _Andrew Howroyd_, Sep 23 2019

%Y Cf. A001221, A293548.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Sep 23 2019