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%I #24 Apr 07 2021 15:49:03
%S 2,3,5,7,13,17,19,23,37,43,61,73,89,103,107,109,139,151,181,197,223,
%T 251,263,307,359,433,613,701,937,997,1033,1213,1249,1321,1601,2053,
%U 2069,2267,2423,2741,2801,3083,3607,3613,3907,4283,4327,4919,5011,5419,6701
%N Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^6) / n is an integer.
%C a(301) > 458158058915101. - _Bruce Garner_, Apr 07 2021
%H Bruce Garner, <a href="/A233041/b233041.txt">Table of n, a(n) for n = 1..300</a> (first 229 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) = 13, because 13 is the 6th prime and the sum of the first 6 primes^6+1 = 6732438 when divided by 6 equals 1122073, which is an integer.
%t t = {}; sm = 1; Do[sm = sm + Prime[n]^6; 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)^6); 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 03 2013
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