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

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

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..9.

OEIS Wiki, Sums of powers of primes divisibility sequences.

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 *)

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.

Sequence in context: A128965 A289345 A063049 * A074868 A277338 A252083

Adjacent sequences: A131271 A131272 A131273 * A131275 A131276 A131277

Keyword

more,nonn,less

Author

Alexander Adamchuk, Jun 25 2007

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

Status

approved