A233349 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^13.

1, 2, 4, 6, 10, 12, 52, 74, 136, 242, 305, 670, 1431, 1706, 1713, 3956, 18331, 22238, 25162, 107332, 162778, 169479, 431228, 459704, 1808681, 1813273, 5954563, 10351930, 27931668, 32490143, 201039164, 311357190, 733854046, 1677164490, 3722808264, 9000784596

Offset: 1

Author

Robert Price, Dec 07 2013

Keywords

• nonn

Comments

a(47) > 1.4*10^13. - Bruce Garner, May 05 2021

Examples

			a(5) = 10 because 1 plus the sum of the first 10 primes^13 is 10816960132320284800 which is divisible by 10.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..46
• 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^13; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)