A329437 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*prime(j)))).

0, 1, 1, 2, 2, 4, 3, 5, 5, 8, 6, 12, 9, 14, 15, 19, 17, 27, 23, 35, 34, 42, 40, 61, 54, 70, 72, 92, 87, 121, 111, 143, 147, 175, 180, 232, 219, 268, 282, 340, 336, 419, 413, 499, 523, 598, 614, 752, 747, 879, 917, 1058, 1083, 1280, 1306, 1515, 1576, 1783, 1850

Offset

1,4

Comments

Inverse Moebius transform of A000607.

Links

Table of n, a(n) for n=1..59.

Formula

G.f.: Sum_{k>=1} A000607(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000607(d).

Mathematica

nmax = 59; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k Prime[j])), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A000607, A047966, A047968, A329438.

Sequence in context: A262991 A077026 A060026 * A318632 A094051 A159268

Adjacent sequences: A329434 A329435 A329436 * A329438 A329439 A329440

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved