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A233577 Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^18) / n is an integer. 1

%I

%S 2,3,5,7,13,17,19,23,37,43,61,67,73,89,103,107,151,163,179,181,197,

%T 223,251,263,269,307,347,359,373,383,433,491,587,593,613,619,701,751,

%U 761,881,997,1019,1129,1321,1439,1601,1699,1951,2069,2243,2267,2297,2423

%N Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^18) / n is an integer.

%C a(516) > 1066173339601.

%H Robert Price, <a href="/A233577/b233577.txt">Table of n, a(n) for n = 1..515</a>

%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^18+1 = 118016956494132483318 when divided by 6 equals 19669492749022080553 which is an integer.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^18; 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)^18); 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 13 2013

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Last modified January 25 01:44 EST 2020. Contains 331229 sequences. (Running on oeis4.)