A233041 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^6) / n is an integer.

2, 3, 5, 7, 13, 17, 19, 23, 37, 43, 61, 73, 89, 103, 107, 109, 139, 151, 181, 197, 223, 251, 263, 307, 359, 433, 613, 701, 937, 997, 1033, 1213, 1249, 1321, 1601, 2053, 2069, 2267, 2423, 2741, 2801, 3083, 3607, 3613, 3907, 4283, 4327, 4919, 5011, 5419, 6701

Offset: 1

Author

Robert Price, Dec 03 2013

Keywords

• nonn

Comments

a(301) > 458158058915101. - Bruce Garner, Apr 07 2021

Examples

			a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^6+1 = 6732438 when divided by 6 equals 1122073, which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..300 (first 229 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]^6; 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)^6); s==0 \\ Charles R Greathouse IV, Nov 30 2013