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 A233863 #31 Mar 29 2022 18:22:26
%S A233863 2,3,7,11,13,29,37,43,257,421,449,7333,7673,9433,9539,12163,53551,
%T A233863 74759,119429,199909,295703,2494781,6941633,39150679,50026091,
%U A233863 165204709,410054731,724768817,1282680871,1777452847,2923304383,6053209493,7423469173,35896955599,46936773853
%N A233863 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^3) / n is an integer.
%C A233863 a(50) > 730228645826551. - _Bruce Garner_, Apr 04 2021
%C A233863 a(55) > 7824556240506443. - _Bruce Garner_, Mar 28 2022
%H A233863 Bruce Garner, <a href="/A233863/b233863.txt">Table of n, a(n) for n = 1..54</a>
%H A233863 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A233863 a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^3+1 = 4032 when divided by 6 equals 672 which is an integer.
%t A233863 t = {}; sm = 1; Do[sm = sm + Prime[n]^3; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%t A233863 Module[{nn=7500,pt},pt=1+Accumulate[Prime[Range[nn]]^3];Prime[#]&/@ Select[ Thread[{pt,Range[nn]}],Divisible[#[[1]],#[[2]]]&]][[All,2]] (* The program generates the first 18 terms of the sequence. It is not suitable for generating many more. *) (* _Harvey P. Dale_, Mar 17 2022 *)
%o A233863 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^3); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y A233863 Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y A233863 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233863 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233863 nonn
%O A233863 1,1
%A A233863 _Robert Price_, Dec 16 2013