A288570 Partial sums of A019565.

1, 3, 6, 12, 17, 27, 42, 72, 79, 93, 114, 156, 191, 261, 366, 576, 587, 609, 642, 708, 763, 873, 1038, 1368, 1445, 1599, 1830, 2292, 2677, 3447, 4602, 6912, 6925, 6951, 6990, 7068, 7133, 7263, 7458, 7848, 7939, 8121, 8394, 8940, 9395, 10305, 11670, 14400, 14543

Offset: 0

Author

N. J. A. Sloane, Jun 26 2017

Keywords

• nonn
• look

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A019565.

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A288570(n) = sum(i=0,n,A019565(i)); \\ Antti Karttunen, Aug 19 2021

Formula

G.f.: (1/(1 - x)) * Product_{k>=0} (1 + prime(k+1)*x^(2^k)). - Ilya Gutkovskiy, Aug 18 2021