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 A233577 #34 Jun 06 2021 15:50:59
%S A233577 2,3,5,7,13,17,19,23,37,43,61,67,73,89,103,107,151,163,179,181,197,
%T A233577 223,251,263,269,307,347,359,373,383,433,491,587,593,613,619,701,751,
%U A233577 761,881,997,1019,1129,1321,1439,1601,1699,1951,2069,2243,2267,2297,2423
%N A233577 Prime(k), where k is such that (1+Sum_{i=1..k} prime(i)^18) / k is an integer.
%C A233577 a(681) > 491952295618219. - _Bruce Garner_, Jun 06 2021
%H A233577 Bruce Garner, <a href="/A233577/b233577.txt">Table of n, a(n) for n = 1..680</a> (first 515 terms from Robert Price, terms 516..559 from Karl-Heinz Hofmann)
%H A233577 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A233577 13 is a term because 13 is the 6th prime and the sum of the first 6 primes^18+1 = 118016956494132483318 when divided by 6 equals 19669492749022080553 which is an integer.
%t A233577 t = {}; sm = 1; Do[sm = sm + Prime[n]^18; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A233577 (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
%Y A233577 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A233577 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233577 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233577 nonn
%O A233577 1,1
%A A233577 _Robert Price_, Dec 13 2013