A352003 Expansion of e.g.f. Product_{k>=1} (1 + x^prime(k))^(1/prime(k)).

1, 0, 1, 2, -3, 44, -35, 1014, -1127, 46808, 153081, 3240170, -30922859, 443621892, 331421077, 121899383774, 691635821745, 19657393214384, 424491327098353, 2132527815161298, -2864544697983059, 3885322666246386140, 22621061924336157261, 882556261002776755142

Offset: 0

Author

Seiichi Manyama, Feb 28 2022

Keywords

• sign

Crossrefs

Cf. A168243, A305614, A318913, A352005.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+isprime(k)*x^k)^(1/k))))

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, isprime(d)*(-1)^(k/d+1))*x^k/k))))

Formula

E.g.f.: exp( Sum_{k>=1} A305614(k)*x^k/k ) where A305614(k) = Sum_{p|k, p prime} (-1)^(k/p+1).