A234003 - OEIS

%I #31 Mar 29 2022 17:17:23

%S 2,3,7,13,29,37,79,271,907,2447,3301,4969,9241,26111,27941,38039,

%T 58603,90071,243469,617579,849143,6994363,10661177,68783413,122137849,

%U 131221879,187987693,194658539,283102597,329015387,1682202323,5230637117,5461627177,32315983207,69900989237,154638658121,227225999443,306462968363,349585319959,1128669425707,1245067407509

%N Prime(n), where n is such that (1+Sum_{i=1..n} prime(i)^5) / n is an integer.

%C a(52) > 1005368767096627. - _Bruce Garner_, Jun 05 2021

%C a(53) > 4193009611262897. - _Bruce Garner_, Mar 28 2022

%H Bruce Garner, <a href="/A234003/b234003.txt">Table of n, a(n) for n = 1..52</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(4) = 13, because 13 is the 6th prime and the sum of the first 6 primes^5 + 1 = 552552 when divided by 6 equals 92092 which is an integer.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^5; 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)^5); 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 18 2013