A300521 Expansion of Product_{k>=1} (1 - x^prime(k))^prime(k).

1, 0, -2, -3, 1, 1, 3, 0, 9, 8, 4, -31, -12, -13, 20, -13, 48, -17, 74, -87, 8, -143, 175, -174, 349, -164, 369, -651, 520, -1004, 1142, -1218, 1652, -1739, 3291, -3933, 3546, -5743, 6170, -8022, 11435, -13230, 17196, -18706, 22958, -31884, 38420, -49802, 58916

Offset

0,3

Links

Table of n, a(n) for n=0..48.

Formula

G.f.: Product_{k>=1} (1 - x^A000040(k))^A000040(k).

G.f.: exp(-Sum_{k>=1} A005063(k)*x^k/k).

Mathematica

nmax = 48; CoefficientList[Series[Product[(1 - x^Prime[k])^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 48; CoefficientList[Series[Exp[-Sum[DivisorSum[k, Boole[PrimeQ[#]] #^2 &] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]

Crossrefs

Cf. A000040, A000607, A005063, A007441, A030009, A046675, A073592, A219224, A291647, A291696.

Sequence in context: A256187 A308297 A251045 * A356152 A317627 A271566

Adjacent sequences: A300518 A300519 A300520 * A300522 A300523 A300524

Keyword

sign

Author

Ilya Gutkovskiy, Mar 08 2018

Status

approved