A131276 Numbers m such that m divides Sum_{k=1..m} prime(k)^16.

1, 3131, 6289, 323807, 443371, 83802527023, 4076111200313

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• more
• nonn
• less

Comments

a(7) > 10^11. - Paul W. Dyson, Dec 30 2020

a(8) > 4.1*10^12. - Bruce Garner, Mar 24 2021

a(8) > 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]^16; If[ Mod[s, n] == 0, Print[n]], {n, 500000}]
Transpose[Select[With[{nn=500000},Thread[{Range[nn],Accumulate[ Prime[ Range[nn]]^16]}]], Divisible[ #[[2]],#[[1]]]&]][[1]]

Extensions

a(6) from Paul W. Dyson, Dec 30 2020

a(7) from Bruce Garner, Mar 24 2021