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%I #23 Jun 06 2021 15:51:11
%S 2,3,5,7,11,13,19,23,29,37,47,53,59,71,89,103,113,131,139,167,173,197,
%T 223,233,257,269,281,311,337,409,439,463,503,541,557,659,719,769,941,
%U 997,1013,1069,1109,1163,1249,1259,1321,1451,1493,1511,1613,1747,1867
%N Prime(n), where n is such that (1+Sum_{i=1..n} prime(i)^16) / n is an integer.
%C a(616) > 491952295618219. - _Bruce Garner_, Jun 06 2021
%H Bruce Garner, <a href="/A233462/b233462.txt">Table of n, a(n) for n = 1..615</a> (first 479 terms from Robert Price)
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e a(5) = 11, because 11 is the 5th prime and the sum of the first 5 primes^16+1 = 45983115425144645 when divided by 5 equals 9196623085028929 which is an integer.
%t t = {}; sm = 1; Do[sm = sm + Prime[n]^16; 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)^16); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn
%O 1,1
%A _Robert Price_, Dec 10 2013