A233193 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^11.

1, 2, 4, 5, 6, 10, 12, 17, 22, 45, 87, 217, 546, 17806, 41850, 127973, 189586, 435067, 475810, 595932, 3319478, 3737221, 5741156, 7349730, 7473734, 13114674, 26076896, 48515830, 48791555, 419983404, 2217443166, 2617207503, 2894318150, 8776851351, 118596802796

Offset: 1

Author

Robert Price, Dec 05 2013

Keywords

• nonn

Comments

a(47) > 3*10^13. - Bruce Garner, Jun 05 2021

Examples

			a(5)=6 because 1 plus the sum of the first 6 primes^11 is 2079498398712  which is divisible by 6.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..46
• 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 < 41000000000, s = s + p^11; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
With[{nn = 5*10^7},Select[Thread[{Accumulate[ Prime[ Range[nn]]^11] + 1, Range[nn]}], Divisible[#[[1]], #[[2]]] &][[All, 2]]] (* The program generates the first 29 terms of the sequence. To generate all 34, change the value of nn to 878*10^7, but the program will take a long time to run. *) (* Harvey P. Dale, Mar 09 2017 *)

Extensions

a(35) from Karl-Heinz Hofmann, Mar 07 2021