A232823 Numbers k such that k divides 1 + Sum_{j=1..k} (prime(j)^8).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 24, 28, 30, 32, 37, 39, 40, 45, 48, 60, 64, 80, 90, 96, 100, 104, 120, 133, 160, 168, 174, 180, 205, 211, 240, 247, 320, 360, 456, 480, 512, 540, 560, 563, 580, 676, 692, 735, 820, 864, 930, 960, 1215, 1216, 1368

Offset: 1

Author

Robert Price, Nov 30 2013

Keywords

• nonn

Comments

a(305) > 1.2*10^14. - Bruce Garner, Mar 20 2022

Examples

			a(7)=8 because 1 plus the sum of the first 8 primes^8 is 24995572328 which is divisible by 8.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..304 (terms 1..227 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 < 521330000, s = s + p^8; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p](* Derived from A128169 *)
With[{nn=1400},Select[Thread[{Range[nn],Accumulate[Prime[Range[nn]]^8]+1}],Mod[ #[[2]],#[[1]]] == 0&]][[;;,1]] (* Harvey P. Dale, Jul 20 2024 *)