A131274 Numbers m such that m divides Sum_{k=1..m} prime(k)^14.

1, 295, 455, 4361, 10817, 132680789, 334931875, 957643538339, 82185210732157

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• more
• nonn
• less

Comments

a(8) > 4.1*10^10. - Robert Price, Dec 02 2013

a(9) > 10^12. - Paul W. Dyson, Jan 03 2021

a(10) > 2*10^15. - Paul W. Dyson, Nov 23 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]^14; If[ Mod[s, n] == 0, Print[n]], {n, 660000000}] (* Robert G. Wilson v, Jul 01 2007 *)
With[{nn=11000},Select[Thread[{Accumulate[Prime[Range[nn]]^14],Range[ nn]}],Divisible[ #[[1]],#[[2]]]&]][[All,2]] (* The program generates the first 5 terms of the sequence. To generate more, increase the value of nn. *) (* Harvey P. Dale, Jun 25 2021 *)

Extensions

a(6) from Robert G. Wilson v, Jul 01 2007

a(7) from Robert Price, Dec 02 2013

a(8) from Paul W. Dyson, Jan 03 2021

a(9) from Bruce Garner, Mar 28 2022