A233768 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^19.

1, 2, 4, 5, 6, 10, 12, 53, 226, 361, 400, 620, 935, 1037, 3832, 3960, 4956, 7222, 12183, 13615, 24437, 80849, 450827, 680044, 7388490, 23503578, 27723887, 52048944, 85860268, 126177976, 606788411, 613917734, 2693408896, 3856356590, 5167833600, 5810025660, 9197308014, 10805855623, 19751202045, 19781610414, 27240188169, 30742119459

Offset: 1

Author

Robert Price, Dec 15 2013

Keywords

• nonn

Comments

a(51) > 1.5*10^13. - Bruce Garner, Jun 02 2021

Examples

			6 is a term because 1 plus the sum of the first 6 primes^19 is 1523090798793695143992 which is divisible by 6.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..50 (first 42 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^19; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
Module[{nn=74*10^5,apr},apr=Accumulate[Prime[Range[nn]]^19];Select[Range[ nn],Divisible[1+apr[[#]],#]&]] (* The program generates the first 25 terms of the sequence. To generate more, increase the value of nn, but the program may take a long time to run. *) (* Harvey P. Dale, Oct 02 2021 *)