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 A232824 #33 Aug 25 2024 12:25:04
%S A232824 2,3,5,7,11,13,19,23,29,37,47,53,71,89,107,113,131,157,167,173,197,
%T A232824 223,281,311,409,463,503,541,569,659,751,941,997,1033,1069,1259,1297,
%U A232824 1511,1567,2129,2423,3221,3413,3671,3907,4057,4091,4231,5051,5197,5569
%N A232824 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^8) / k is an integer.
%C A232824 a(305) > 4193009611262897. - _Bruce Garner_, Mar 20 2022
%H A232824 Bruce Garner, <a href="/A232824/b232824.txt">Table of n, a(n) for n = 1..304</a> (terms 1..227 from Robert Price)
%H A232824 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A232824 a(5) = 11, because 11 is the 5th prime and the sum of the first 5 primes^8+1 = 220521125 when divided by 5 equals 44104225 which is an integer.
%t A232824 t = {}; sm = 1; Do[sm = sm + Prime[n]^8; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%t A232824 Prime[#]&/@Flatten[Position[Table[(1+Sum[Prime[n]^8,{n,k}])/k,{k,800}],_?IntegerQ]] (* _Harvey P. Dale_, Aug 25 2024 *)
%o A232824 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^8); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y A232824 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A232824 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A232824 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A232824 nonn
%O A232824 1,1
%A A232824 _Robert Price_, Nov 30 2013