A327725 Expansion of Product_{i>=1, j>=1} (1 + x^(i*prime(j))).

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, 195, 235, 276, 329, 394, 460, 546, 646, 753, 890, 1044, 1214, 1422, 1662, 1927, 2245, 2611, 3015, 3497, 4051, 4662, 5385, 6209, 7128, 8203, 9423, 10786

Offset

0,6

Comments

Weigh transform of A001221.

Links

Table of n, a(n) for n=0..52.

Formula

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

Mathematica

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

Prog

(PARI) seq(n)={Vec(prod(k=1, n, (1 + x^k + O(x*x^n))^omega(k)))} \\ Andrew Howroyd, Sep 23 2019

Crossrefs

Cf. A001221, A293548.

Sequence in context: A358993 A198726 A117275 * A253926 A277579 A241447

Adjacent sequences: A327722 A327723 A327724 * A327726 A327727 A327728

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2019

Status

approved