A233556 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^17.

1, 2, 4, 6, 10, 12, 116, 147, 324, 2070, 2902, 3663, 4994, 11531, 13554, 22421, 558905, 1242890, 1655487, 2021278, 2878297, 4790338, 7061177, 16875261, 21813642, 24563860, 58919808, 69676102, 85356321, 92610708, 205600836, 338430087, 343675600, 1176903461, 1698127637, 4657254361, 17421656611

Offset: 1

Author

Robert Price, Dec 12 2013

Keywords

• nonn

Comments

a(45) > 1.5*10^13. - Bruce Garner, Jun 02 2021

Examples

			10 is a term because 1 plus the sum of the first 10 primes^17 is 7404514559506748686057600 which is divisible by 10.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..44 (first 37 terms from Robert Price, terms 38..39 from Karl-Heinz Hofmann)
• 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^17; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)