A224083 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^5) / m is an integer.

2, 97, 6449, 49943, 1220347, 3821963, 60252541, 61785991, 10678796441, 47363940857, 830546726491, 2639027583253, 4087115060797, 4645513891321, 711935349228079, 3393070609976863

Offset: 1

Author

Robert Price, Mar 30 2013

Keywords

• nonn
• more

Comments

a(17) > 3.7*10^16. - Paul W. Dyson, Jan 17 2025

Examples

			a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^5 = 29014217650 when divided by 25 equals 1160568706 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]^5; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

Extensions

a(13)-a(14) from Paul W. Dyson, Jan 04 2021

a(15) from Bruce Garner, May 09 2021

a(16) from Paul W. Dyson, Feb 04 2022