A233413 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^15.

1, 2, 4, 5, 6, 10, 12, 14, 22, 74, 397, 524, 620, 857, 3727, 8171, 9194, 41032, 59604, 109471, 123231, 166394, 195736, 203440, 494620, 805738, 3000362, 6861264, 64286003, 69417562, 113888084, 162292604, 241184820, 658646484, 864667379, 1027008032, 4023976348

Offset: 1

Author

Robert Price, Dec 09 2013

Keywords

• nonn

Comments

a(49) > 2*10^13. - Bruce Garner, Jun 02 2021

Examples

			a(6)=10 because 1 plus the sum of the first 10 primes^15 is 8913922901063237276800 which is divisible by 10.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..48 (first 43 terms from Robert Price)
• 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

p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^15; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)