%I #64 Apr 19 2024 03:25:58
%S 2,59,97,127,12517,54581,83921,89273,1396411,2562719,4952183,29201281,
%T 35562101,47567557,111213143,184201627,1172476337,7309217299,
%U 287609314877,5173838081669,408907258717171,1357729730868191,66413899001789557
%N Prime(k), where k divides Sum_{i=1..k} prime(i)^15.
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F a(n) = prime(A131275(n)).
%e a(2) = 59, because 59 is the 17th prime and the sum of the first 17 primes^15 = 455708280934100194626604550 when divided by 17 equals 26806369466711776154506150 which is an integer.
%t t = {}; sm = 0; Do[sm = sm + Prime[n]^15; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^15); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%o (PARI) S=n=0;forprime(p=1,,(S+=p^15)%n++||print1(p",")) \\ _M. F. Hasler_, Dec 01 2013
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n), A131275.
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn,more
%O 1,1
%A _Robert Price_, Dec 09 2013
%E a(20) from _Karl-Heinz Hofmann_, Feb 17 2021
%E a(21) from _Bruce Garner_, Apr 30 2021
%E a(22) from _Bruce Garner_, Jan 07 2022
%E a(23) from _Paul W. Dyson_, Apr 18 2024