A329438 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*prime(j)))).

0, 1, 1, 1, 2, 2, 2, 2, 2, 5, 1, 4, 2, 5, 5, 5, 2, 7, 3, 9, 7, 6, 5, 10, 7, 9, 7, 11, 7, 14, 9, 12, 11, 12, 13, 20, 11, 15, 16, 22, 14, 25, 15, 23, 22, 24, 19, 33, 23, 33, 25, 34, 26, 39, 33, 41, 36, 40, 35, 57, 39, 50, 50, 56, 49, 66, 50, 65, 61, 75, 61

Offset

1,5

Comments

Inverse Moebius transform of A000586.

Links

Table of n, a(n) for n=1..71.

Formula

G.f.: Sum_{k>=1} A000586(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000586(d).

Mathematica

nmax = 71; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k Prime[j])), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A000586, A047966, A047968, A329437.

Sequence in context: A160419 A152659 A180214 * A263342 A089452 A162487

Adjacent sequences: A329435 A329436 A329437 * A329439 A329440 A329441

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved