A294403 E.g.f.: exp(-Sum_{n>=1} sigma(n) * x^n).

1, -1, -5, -7, 1, 839, 4171, 54305, 102817, -4303441, -74521349, -1595325271, -20768141855, -222701825737, 1485790534411, 65580347824529, 2880129557707201, 67631429234674655, 1543424936566399867, 23542870556917468889, 119940955037901088321

Offset: 0

Author

Seiichi Manyama, Oct 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..439

Crossrefs

E.g.f.: exp(-Sum_{n>=1} sigma_k(n) * x^n): A294402 (k=0), this sequence (k=1), A294404 (k=2).

Cf. A000203, A010815, A069097, A294361.

Programs

PARI

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

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A000203(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)^2. - Ilya Gutkovskiy, Aug 17 2021