A131273 Numbers k that divide Sum_{j=1..k} prime(j)^13.

1, 23, 299, 313, 171287, 435705, 487475, 3774601, 219347813, 9613155161, 5150163868035, 37365789554345, 228914067371295

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• more
• nonn
• less

Comments

a(13) > 4*10^13. - Bruce Garner, Aug 30 2021

a(14) > 5*10^14. - Paul W. Dyson, Dec 06 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]^13; If[ Mod[s, n] == 0, Print[n]], {n, 200000}]

PARI

S=n=0;forprime(p=1,,(S+=p^13)%n++||print1(n",")) \\ M. F. Hasler, Dec 01 2013

Extensions

a(6)-a(8) from Robert G. Wilson v, Jun 30 2007

a(9)-a(10) from Robert Price, Nov 28 2013

a(11) from Bruce Garner, Mar 23 2021

a(12) from Bruce Garner, Aug 30 2021

a(13) from Paul W. Dyson, Apr 20 2023