A233043 - OEIS

%I #20 Jun 02 2021 04:21:09

%S 2,3,5,7,13,19,23,37,41,89,101,107,197,223,457,997,2423,3361,3907,

%T 3989,6701,8861,10007,11731,12473,15569,21031,24071,32693,55009,58427,

%U 66293,119267,138967,153191,268531,275581,316961,499853,525313,705259,946873

%N Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^14) / n is an integer.

%C a(120) > 661876608760109. - _Bruce Garner_, Jun 02 2021

%H Bruce Garner, <a href="/A233043/b233043.txt">Table of n, a(n) for n = 1..119</a> (first 101 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^14+1 = 4317810550670358 when divided by 6 equals 719635091778393 which is an integer.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^14; 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)^14); 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