A233576 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^18.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 19, 21, 24, 27, 28, 36, 38, 41, 42, 45, 48, 54, 56, 57, 63, 69, 72, 74, 76, 84, 94, 107, 108, 112, 114, 126, 133, 135, 152, 168, 171, 189, 216, 228, 252, 266, 297, 312, 334, 336, 342, 360, 378, 380, 399, 423, 432, 441, 444

Offset: 1

Author

Robert Price, Dec 13 2013

Keywords

• nonn

Comments

a(681) > 1.5*10^13. - Bruce Garner, Jun 06 2021

Examples

			6 is a term because 1 plus the sum of the first 6 primes^18 is 118016956494132483318 which is divisible by 6.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..680 (first 515 terms from Robert Price, terms 516..559 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^18; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)