A232966 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^14.

1, 2, 3, 4, 6, 8, 9, 12, 13, 24, 26, 28, 45, 48, 88, 168, 360, 474, 540, 550, 864, 1104, 1230, 1408, 1488, 1816, 2367, 2677, 3507, 5592, 5916, 6612, 11238, 12925, 14124, 23523, 24087, 27356, 41528, 43465, 56951, 74688, 79244, 86682, 181730, 186136, 193704

Offset: 1

Author

Robert Price, Dec 02 2013

Keywords

• nonn

Comments

a(120) > 2*10^13. - Bruce Garner, Jun 02 2021

Examples

			a(7)=9 because 1 plus the sum of the first 9 primes^14 is 12564538647431705217 which is divisible by 9.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..119 (first 101 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^14; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)