This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A232770 #34 Dec 06 2024 20:18:50
%S A232770 2,83,1979,2081,2326469,6356923,7170679,63812027,4652001719,
%T A232770 241949473277,163220642765623,1260677492111911,8150959175977039
%N A232770 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer.
%C A232770 a(13) > 1352363608564489. - _Bruce Garner_, Aug 30 2021
%C A232770 a(14) > 18205684894350047. - _Paul W. Dyson_, Dec 06 2024
%H A232770 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A232770 a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 which is an integer.
%t A232770 t = {}; sm = 0; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A232770 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^13); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y A232770 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A232770 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A232770 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A232770 nonn,more
%O A232770 1,1
%A A232770 _Robert Price_, Nov 29 2013
%E A232770 a(11) from _Bruce Garner_, Mar 23 2021
%E A232770 a(12) from _Bruce Garner_, Aug 30 2021
%E A232770 a(13) from _Paul W. Dyson_, Apr 20 2023