A131278 Numbers m such that m divides the sum of the 18th powers of the first m primes.

1, 37, 265, 17207, 9382589, 970248431, 2427811793, 156281194823, 2955922292131, 372012276565795

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• more
• nonn

Comments

a(10) > 3.0*10^12. - Bruce Garner, Mar 17 2021

a(11) > 5*10^14. - Paul W. Dyson, Dec 16 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]^18; If[ Mod[s, n] == 0, Print[n]], {n, 10^6}]
With[{nn = 18000}, Transpose[With[{c = Thread[{Range[nn], Accumulate[Prime[ Range[nn]]^18]}]}, Select[c, Divisible[Last[#], First[#]] &]]][[1]]] (* Harvey P. Dale, Dec 19 2011 *)

Extensions

a(5)-a(7) from Robert Price, Dec 13 2013

a(8) from Paul W. Dyson, Jan 08 2021

a(9) from Bruce Garner, Mar 17 2021

a(10) from Paul W. Dyson, Oct 03 2023