A233264 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^12.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 24, 26, 27, 28, 30, 35, 36, 39, 40, 42, 45, 46, 48, 52, 54, 56, 60, 63, 65, 66, 70, 72, 78, 80, 84, 87, 90, 91, 100, 104, 105, 112, 117, 120, 126, 130, 138, 140, 144, 154, 156, 160, 168, 175, 176

Offset: 1

Author

Robert Price, Dec 06 2013

Keywords

• nonn

Comments

a(1171) > 2*10^13. - Bruce Garner, Jun 06 2021

Examples

			5 is a term because 1 plus the sum of the first 11 primes^12 is 3152514340085 which is divisible by 11.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..1170 (terms 1..907 from Robert Price, terms 908..967 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

Maple

A233264:=n->if type((1+add(ithprime(i)^12, i=1..n))/n, integer) then n; fi; seq(A233264(n), n=1..200); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^12; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
With[{nn=200},Transpose[Select[Thread[{Accumulate[Prime[Range[nn]]^12], Range[nn]}], Divisible[#[[1]]+1,#[[2]]]&]][[2]]] (* Harvey P. Dale, May 28 2015 *)