A232964 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^9.

1, 2, 4, 6, 10, 12, 14, 82, 93, 476, 712, 856, 935, 11104, 11706, 12234, 19500, 21490, 31864, 171252, 628863, 10189718, 12363588, 13976077, 22321041, 36642393, 47563206, 102352700, 869166585, 1197804361, 1400403575, 2199080290, 5225532140, 39957170689

Offset: 1

Author

Robert Price, Dec 02 2013

Keywords

• nonn

Comments

a(49) > 3*10^13. - Bruce Garner, Jun 05 2021

Examples

			a(5)=10 because 1 plus the sum of the first 10 primes^9 is 16762578985600 which is divisible by 10.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..48 (first 34 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^9; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)