A024918 Partial sums of the sequence of prime powers (A000961).

1, 3, 6, 10, 15, 22, 30, 39, 50, 63, 79, 96, 115, 138, 163, 190, 219, 250, 282, 319, 360, 403, 450, 499, 552, 611, 672, 736, 803, 874, 947, 1026, 1107, 1190, 1279, 1376, 1477, 1580, 1687, 1796, 1909, 2030, 2155, 2282, 2410, 2541, 2678, 2817, 2966, 3117, 3274, 3437

Offset: 1

Author

Den Roussel (DenRoussel(AT)webtv.net)

Keywords

• nonn

Comments

The subsequence of prime partial sums of prime powers begins: 3, 79, 163, 499, 947, 1279, 5297. What is the smallest value which is a prime power p^k for k>1? [Jonathan Vos Post, Feb 11 2010]

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A024923.

Programs

Mathematica

FoldList[Plus, 1, Select[Range[150], PrimePowerQ]] (* Amiram Eldar, Jun 22 2025 *)

PARI

ispp1(n) = isprimepower(n) || (n==1); \\ A000961
lista(nn) = {my(s=0); for (n=1, nn, if (ispp1(n), s+= n; print1(s, ", ")););} \\ Michel Marcus, Mar 26 2020

Extensions

Offset 1 from Michel Marcus, Mar 26 2020