A233462 Prime(n), where n is such that (1+Sum_{i=1..n} prime(i)^16) / n is an integer.

2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 47, 53, 59, 71, 89, 103, 113, 131, 139, 167, 173, 197, 223, 233, 257, 269, 281, 311, 337, 409, 439, 463, 503, 541, 557, 659, 719, 769, 941, 997, 1013, 1069, 1109, 1163, 1249, 1259, 1321, 1451, 1493, 1511, 1613, 1747, 1867

Offset: 1

Author

Robert Price, Dec 10 2013

Keywords

• nonn

Comments

a(616) > 491952295618219. - Bruce Garner, Jun 06 2021

Examples

			a(5) = 11, because 11 is the 5th prime and the sum of the first 5 primes^16+1 = 45983115425144645 when divided by 5 equals 9196623085028929 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..615 (first 479 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]^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