A234003 Prime(n), where n is such that (1+Sum_{i=1..n} prime(i)^5) / n is an integer.

2, 3, 7, 13, 29, 37, 79, 271, 907, 2447, 3301, 4969, 9241, 26111, 27941, 38039, 58603, 90071, 243469, 617579, 849143, 6994363, 10661177, 68783413, 122137849, 131221879, 187987693, 194658539, 283102597, 329015387, 1682202323, 5230637117, 5461627177, 32315983207, 69900989237, 154638658121, 227225999443, 306462968363, 349585319959, 1128669425707, 1245067407509

Offset: 1

Author

Robert Price, Dec 18 2013

Keywords

• nonn

Comments

a(52) > 1005368767096627. - Bruce Garner, Jun 05 2021

a(53) > 4193009611262897. - Bruce Garner, Mar 28 2022

Examples

			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.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..52
• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^5; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

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