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%I #40 Jun 27 2023 07:06:16
%S 1,25,453,677,839,1015,3735,4175,4413,10369,14239,43311,452567,
%T 1274185,14102849,37801813,71271705,93524231,386557609,2151748733,
%U 261349938459,761474469415,1284262332971,5115376212971,17863411895047,122189141425495
%N Numbers k such that k divides Sum_{j=1..k} prime(j)^19.
%C a(26) > 2*10^13. - _Bruce Garner_, Jun 30 2021
%C a(27) > 1.34*10^14. - _Paul W. Dyson_, Jun 27 2023
%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]^19; If[ Mod[s, n] == 0, Print[n]], {n, 50000}]
%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 _Alexander Adamchuk_, Jun 25 2007
%E More terms from _Ryan Propper_, Oct 09 2007
%E a(19)-a(20) from _Robert Price_, Dec 15 2013
%E a(21) from _Karl-Heinz Hofmann_, Feb 24 2021
%E a(22) from _Bruce Garner_, Mar 01 2021
%E a(23) from _Bruce Garner_, Mar 08 2021
%E a(24) from _Bruce Garner_, Apr 14 2021
%E a(25) from _Bruce Garner_, Jun 30 2021
%E a(26) from _Paul W. Dyson_, Jun 27 2023
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