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%I #29 Oct 02 2021 17:55:38
%S 1,2,4,5,6,10,12,53,226,361,400,620,935,1037,3832,3960,4956,7222,
%T 12183,13615,24437,80849,450827,680044,7388490,23503578,27723887,
%U 52048944,85860268,126177976,606788411,613917734,2693408896,3856356590,5167833600,5810025660,9197308014,10805855623,19751202045,19781610414,27240188169,30742119459
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^19.
%C a(51) > 1.5*10^13. - _Bruce Garner_, Jun 02 2021
%H Bruce Garner, <a href="/A233768/b233768.txt">Table of n, a(n) for n = 1..50</a> (first 42 terms from Robert Price)
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e 6 is a term because 1 plus the sum of the first 6 primes^19 is 1523090798793695143992 which is divisible by 6.
%t 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 *)
%t 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 *)
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn
%O 1,2
%A _Robert Price_, Dec 15 2013
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