A131275 Numbers k such that k divides Sum_{j=1..k} prime(j)^15.

1, 17, 25, 31, 1495, 5555, 8185, 8647, 106841, 187329, 345377, 1811351, 2179119, 2863775, 6368703, 10250821, 59137893, 337430815, 11349203711, 183233304195, 12538656829431, 40154010310477, 1761333303516473

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• more
• nonn
• less

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]^15; If[ Mod[s, n] == 0, Print[n]], {n, 400000}]
With[{nn = 3*10^6},Select[Thread[{Accumulate[Prime[ Range[nn]]^15],Range[ nn]}],Divisible[#[[1]], #[[2]]] &]][[All, 2]] (* This will generate the first 14 terms of the sequence; to generate more, increase the value of nn, but it may take a long time to run. *) (* Harvey P. Dale, Oct 03 2016 *)

Extensions

a(12)-a(17) from Robert G. Wilson v, Jul 02 2007

a(18)-a(19) from Robert Price, Dec 09 2013

a(20) from Karl-Heinz Hofmann, Feb 17 2021

a(21) from Bruce Garner, Apr 30 2021

a(22) from Bruce Garner, Jan 07 2022

a(23) from Paul W. Dyson, Apr 18 2024