A131279 Numbers k such that k divides Sum_{j=1..k} prime(j)^19.

1, 25, 453, 677, 839, 1015, 3735, 4175, 4413, 10369, 14239, 43311, 452567, 1274185, 14102849, 37801813, 71271705, 93524231, 386557609, 2151748733, 261349938459, 761474469415, 1284262332971, 5115376212971, 17863411895047, 122189141425495

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• nonn

Comments

a(26) > 2*10^13. - Bruce Garner, Jun 30 2021

a(27) > 5*10^14. - Paul W. Dyson, Dec 31 2024

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences.

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

s = 0; Do[s = s + Prime[n]^19; If[ Mod[s, n] == 0, Print[n]], {n, 50000}]

Extensions

More terms from Ryan Propper, Oct 09 2007

a(19)-a(20) from Robert Price, Dec 15 2013

a(21) from Karl-Heinz Hofmann, Feb 24 2021

a(22) from Bruce Garner, Mar 01 2021

a(23) from Bruce Garner, Mar 08 2021

a(24) from Bruce Garner, Apr 14 2021

a(25) from Bruce Garner, Jun 30 2021

a(26) from Paul W. Dyson, Jun 27 2023