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%I #36 Jun 06 2021 02:54:09
%S 2,3,13,29,71,79,107,907,3491,4967,7853,61223,80051,81547,90901,
%T 211811,381629,1990007,3220793,4749637,6725027,6784937,34463699,
%U 143691323,185831033,213609173,285336497,442634651,911588849,953122843,1548789581,2153787017
%N Prime(n), where n is such that (1+sum_{i=1..n} prime(i)) / n is an integer.
%C a(50) > 3475385758524527. - _Bruce Garner_, Jun 05 2021
%H Bruce Garner, <a href="/A233523/b233523.txt">Table of n, a(n) for n = 1..49</a> (first 43 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(3) = 13, because 13 is the 6th prime and the sum of the first 6 primes+1 = 42 when divided by 6 equals 7 which is an integer.
%t t = {}; sm = 1; Do[sm = sm + Prime[n]; 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)); 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 15 2013
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