A223936 Numbers prime(m), such that (Sum_{i=1..m} prime(i)^3) / m is an integer.

2, 97, 3877, 4943, 50741, 1487159, 3356117, 131047091863, 449627893189, 906460844407, 61168531626487, 141835115384731, 749668095960389, 1259394274876189, 3849791511371129, 6669425423437787, 11674340378841221, 75041264698436783

Offset: 1

Author

Robert Price, Mar 29 2013

Keywords

• nonn
• more

Examples

			a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^3 = 4696450 when divided by 25 equals 187858 which is an integer.
		

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 (smallest m > 1 that 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

k = 1; p = 2; s = 0; lst = {}; While[p < 1000000000, s = s + p^3; If[ Mod[s, k++] == 0, AppendTo[lst, p]]; p = NextPrime@ p]; lst

Extensions

a(11) from Paul W. Dyson, Jan 05 2021

a(12) from Bruce Garner, Mar 01 2021

a(13) from Bruce Garner, Apr 06 2021

a(14) from Bruce Garner, May 13 2021

a(15) from Bruce Garner, Jan 08 2022

a(16) from Paul W. Dyson, Jan 17 2022

a(17) from Bruce Garner, Jul 31 2022

a(18) from Paul W. Dyson, Feb 18 2024