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 A232963 #23 Jan 17 2025 22:32:14
%S A232963 2,1933,3217,41681,114311,2743691233,7252463461,28682755720447,
%T A232963 2839633449523319
%N A232963 Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.
%C A232963 The primes correspond to indices n = 1, 295, 455, 4361, 10817, 132680789, 334931875, 957643538339 = A131274.
%C A232963 a(10) > 7.6*10^16. - _Paul W. Dyson_, Jan 17 2025
%H A232963 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F A232963 a(n) = prime(A131274(n)).
%e A232963 a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.
%t A232963 t = {}; sm = 0; Do[sm = sm + Prime[n]^14; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A232963 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^14); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%o A232963 (PARI) S=n=0;forprime(p=1,,(S+=p^14)%n++||print1(p",")) \\ _M. F. Hasler_, Dec 01 2013
%Y A232963 Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y A232963 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A232963 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A232963 nonn,more
%O A232963 1,1
%A A232963 _Robert Price_, Dec 02 2013
%E A232963 a(8) from _Paul W. Dyson_, Jan 03 2021
%E A232963 a(9) from _Bruce Garner_, Mar 28 2022