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A352003
Expansion of e.g.f. Product_{k>=1} (1 + x^prime(k))^(1/prime(k)).
1
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
0,4
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).
PROG
(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))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 28 2022
STATUS
approved