A291647 -id:A291647 - cp's OEIS frontend

A301971 a(n) = [x^n] Product_{k>=1} 1/(1 - x^prime(k))^n.

1, 0, 2, 3, 10, 30, 77, 252, 682, 2136, 6182, 18766, 56173, 169351, 512990, 1551828, 4720170, 14348289, 43751984, 133502873, 408029510, 1248460587, 3823949824, 11724787763, 35980251181, 110510334780, 339674840715, 1044812449722, 3215861978150, 9904301974294, 30521063942312, 94103983534015

Offset: 0

Ilya Gutkovskiy, Mar 29 2018

nonn

Number of partitions of n into prime parts of n kinds.

Index entries for sequences related to partitions

Cf. A000607, A008485, A030009, A117278, A219224, A259254, A291647, A298436, A299168.

Table[SeriesCoefficient[Product[1/(1 - x^Prime[k])^n, {k, 1, n}], {x, 0, n}], {n, 0, 31}]

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Mar 08 2018

sign

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

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]

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

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

cp's OEIS Frontend

A301971 a(n) = [x^n] Product_{k>=1} 1/(1 - x^prime(k))^n.

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