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 A224083 #26 Jan 17 2025 22:32:18
%S A224083 2,97,6449,49943,1220347,3821963,60252541,61785991,10678796441,
%T A224083 47363940857,830546726491,2639027583253,4087115060797,4645513891321,
%U A224083 711935349228079,3393070609976863
%N A224083 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^5) / m is an integer.
%C A224083 a(17) > 3.7*10^16. - _Paul W. Dyson_, Jan 17 2025
%H A224083 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A224083 a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^5 = 29014217650 when divided by 25 equals 1160568706 which is an integer.
%t A224083 t = {}; sm = 0; Do[sm = sm + Prime[n]^5; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%Y A224083 Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y A224083 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A224083 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A224083 nonn,more
%O A224083 1,1
%A A224083 _Robert Price_, Mar 30 2013
%E A224083 a(13)-a(14) from _Paul W. Dyson_, Jan 04 2021
%E A224083 a(15) from _Bruce Garner_, May 09 2021
%E A224083 a(16) from _Paul W. Dyson_, Feb 04 2022