A233040 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^7) / n is an integer.

2, 3, 7, 11, 13, 29, 37, 199, 15679, 18211, 59359, 78203, 84533, 166399, 528299, 639697, 2080651, 2914033, 5687413, 73463179, 112760273, 156196991, 278840981, 503948113, 3706314893, 3786209711, 12626179519, 13551633533, 13844655553, 24074338279, 37937104823

Offset: 1

Author

Robert Price, Dec 03 2013

Keywords

• nonn

Comments

a(43) > 458158058915101. - Bruce Garner, Apr 07 2021

Examples

			a(4) = 11, because 11 is the 5th prime and the sum of the first 5 primes^7+1 = 20391155 when divided by 5 equals 4078231, which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..42 (first 35 terms from Robert Price)
• 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]^7; 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)^7); s==0 \\ Charles R Greathouse IV, Nov 30 2013