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A232770 Prime(n), where n is such that (sum_{i=1..n} prime(i)^13) / n is an integer. 0

%I

%S 2,83,1979,2081,2326469,6356923,7170679,63812027,4652001719,

%T 241949473277

%N Prime(n), where n is such that (sum_{i=1..n} prime(i)^13) / n is an integer.

%C a(11) > 1066173339601.

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%e a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 which is an integer.

%t t = {}; sm = 0; Do[sm = sm + Prime[n]^13; 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)^13); 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,more

%O 1,1

%A _Robert Price_, Nov 29 2013

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Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)