A223936 - OEIS

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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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..18.

OEIS Wiki, Sums of powers of primes divisibility sequences

EXAMPLE

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.

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

CROSSREFS

Cf. A085450 (smallest m > 1 that divides Sum_{k=1..m} prime(k)^n).