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%I #31 Jun 02 2021 05:06:00
%S 1,2,4,5,6,10,12,14,22,74,397,524,620,857,3727,8171,9194,41032,59604,
%T 109471,123231,166394,195736,203440,494620,805738,3000362,6861264,
%U 64286003,69417562,113888084,162292604,241184820,658646484,864667379,1027008032,4023976348
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^15.
%C a(49) > 2*10^13. - _Bruce Garner_, Jun 02 2021
%H Bruce Garner, <a href="/A233413/b233413.txt">Table of n, a(n) for n = 1..48</a> (first 43 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 a(6)=10 because 1 plus the sum of the first 10 primes^15 is 8913922901063237276800 which is divisible by 10.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^15; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
%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 09 2013