A233043 Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^14) / n is an integer.

2, 3, 5, 7, 13, 19, 23, 37, 41, 89, 101, 107, 197, 223, 457, 997, 2423, 3361, 3907, 3989, 6701, 8861, 10007, 11731, 12473, 15569, 21031, 24071, 32693, 55009, 58427, 66293, 119267, 138967, 153191, 268531, 275581, 316961, 499853, 525313, 705259, 946873

Offset: 1

Author

Robert Price, Dec 03 2013

Keywords

• nonn

Comments

a(120) > 661876608760109. - Bruce Garner, Jun 02 2021

Examples

			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.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..119 (first 101 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]^14; 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)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013