A318969 - OEIS

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A318969

Expansion of exp(Sum_{k>=1} ( Sum_{p|k, p prime} p^k ) * x^k/k).

1, 0, 2, 9, 6, 643, 182, 118953, 6019, 242630, 2243190, 25938251679, 78106516, 23349992199606, 288964822371, 46755212195033, 226472341461312, 48661337027901364945, 18066374340919781, 104224677113940850317679, 440728415311733637734, 208546898802899685866735, 972477473959172989443327

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

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

MATHEMATICA

nmax = 22; CoefficientList[Series[Exp[Sum[Sum[Boole[PrimeQ[d]] d^k, {d, Divisors[k]}] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]

nmax = 22; CoefficientList[Series[Product[1/(1 - Prime[k]^Prime[k] x^Prime[k])^(1/Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[Boole[PrimeQ[d]] d^k, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 22}]

CROSSREFS