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%I #39 Apr 21 2023 02:04:53
%S 1,23,299,313,171287,435705,487475,3774601,219347813,9613155161,
%T 5150163868035,37365789554345,228914067371295
%N Numbers k that divide Sum_{j=1..k} prime(j)^13.
%C a(13) > 4*10^13. - _Bruce Garner_, Aug 30 2021
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>.
%t s = 0; Do[s = s + Prime[n]^13; If[ Mod[s, n] == 0, Print[n]], {n, 200000}]
%o (PARI) S=n=0;forprime(p=1,,(S+=p^13)%n++||print1(n",")) \\ _M. F. Hasler_, Dec 01 2013
%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 more,nonn,less
%O 1,2
%A _Alexander Adamchuk_, Jun 25 2007
%E a(6)-a(8) from _Robert G. Wilson v_, Jun 30 2007
%E a(9)-a(10) from _Robert Price_, Nov 28 2013
%E a(11) from _Bruce Garner_, Mar 23 2021
%E a(12) from _Bruce Garner_, Aug 30 2021
%E a(13) from _Paul W. Dyson_, Apr 20 2023
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