A353164 Expansion of 1/(1 - Sum_{p prime} p * x^p).

1, 0, 2, 3, 4, 17, 17, 63, 100, 211, 495, 846, 2057, 3831, 8181, 17078, 33788, 72705, 144801, 303452, 623115, 1274365, 2652052, 5408046, 11207927, 23020231, 47378495, 97774736, 200819019, 414365805, 852285510, 1755453858, 3616014678, 7441523271, 15332278869

Offset: 0

Author

Seiichi Manyama, Apr 28 2022

Keywords

• nonn

Crossrefs

Cf. A000040, A023360, A088305, A353162, A353165.

Programs

PARI

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

PARI

a(n) = if(n==0, 1, sum(k=1, n, isprime(k)*k*a(n-k)));

Formula

a(0) = 1; a(n) = Sum_{p<=n, p prime} p * a(n-p).