A128169 -id:A128169 - cp's OEIS frontend

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

Robert Price, Dec 13 2013

nonn

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

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

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

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.

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 *)

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

Original entry on oeis.org

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

Robert Price, Dec 15 2013

nonn

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

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

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

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.

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 *)

cp's OEIS Frontend

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

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