A233460 Prime(n), where n is such that (sum_{i=1..n} prime(i)^16) / n is an integer.

2, 28751, 62639, 4620757, 6478193, 2298168044423, 128195718927553

Offset: 1

Author

Robert Price, Dec 10 2013

Keywords

• nonn
• more

Comments

a(8) > 128971810356197. - Bruce Garner, Mar 24 2021

a(8) > 7.6*10^16. - Paul W. Dyson, Nov 27 2024

Examples

			a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^16 = 65536 when divided by 1 equals 65536 which is an integer.
		

Links

• 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 = 0; Do[sm = sm + Prime[n]^16; 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)^16); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^16)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131276(n)).

Extensions

a(6)-a(7) from Bruce Garner, Mar 24 2021