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 A233575 #25 Dec 17 2024 00:50:37
%S A233575 2,157,1697,190573,167719729,22092660553,57613776809,4386989244577,
%T A233575 91982826261331,13432259712845291
%N A233575 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^18) / m is an integer.
%C A233575 a(9) > 36730498487251. - _Paul W. Dyson_, Jan 08 2021
%C A233575 a(10) > 93400375993241. - _Bruce Garner_, Mar 17 2021
%C A233575 a(11) > 18205684894350047. - _Paul W. Dyson_, Dec 16 2024
%H A233575 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F A233575 a(n) = prime(A131278(n)).
%e A233575 a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^18 = 7222759943091280921446062146835136523956 when divided by 37 equals 195209728191656241120163841806355041188 which is an integer.
%t A233575 t = {}; sm = 0; Do[sm = sm + Prime[n]^18; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A233575 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^18); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%o A233575 (PARI) S=n=0;forprime(p=1,,(S+=p^18)%n++||print1(p",")) \\ - _M. F. Hasler_, Dec 01 2013
%Y A233575 Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y A233575 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233575 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233575 nonn,more
%O A233575 1,1
%A A233575 _Robert Price_, Dec 13 2013
%E A233575 a(8) from _Paul W. Dyson_, Jan 08 2021
%E A233575 a(9) from _Bruce Garner_, Mar 17 2021
%E A233575 a(10) from _Paul W. Dyson_, Oct 03 2023