A294402 E.g.f.: exp(-Sum_{n>=1} d(n) * x^n), where d(n) is the number of divisors of n.

1, -1, -3, -1, 1, 279, 301, 12263, 5601, -431281, -2140739, -77720721, -1755429983, -12569445721, 85768062381, -4458503862121, 43351731658561, 546719071653663, 31735514726673661, 291860504886837599, 5860390638855992001, 208620917963122666679

Offset: 0

Author

Seiichi Manyama, Oct 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..448

Crossrefs

E.g.f.: exp(-Sum_{n>=1} sigma_k(n) * x^n): this sequence (k=0), A294403 (k=1), A294404 (k=2).

Cf. A000005, A018804, A028343, A294363.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(-sum(k=1, N, numdiv(k)*x^k))))

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A000005(k)*a(n-k)/(n-k)! for n > 0.

E.g.f.: Product_{k>=1} (1 - x^k)^f(k), where f(k) = (1/k) * Sum_{j=1..k} gcd(k,j). - Ilya Gutkovskiy, Aug 17 2021