A217599 Prime(n), where n is such that (Sum_{i=1..n} prime(i)^2) / n is an integer.

2, 67, 157, 3217, 3637, 4201, 231947, 2790569, 30116309, 12021325961, 26144296151, 1380187561637, 6549419699279, 735325088697473, 1746583001138813, 68725636353488501

Offset

1,1

Comments

a(16) > 3*10^15 if it exists. - Anders Kaseorg, Dec 02 2020

Links

Table of n, a(n) for n=1..16.

OEIS Wiki, Sums of powers of primes divisibility sequences

Example

a(2) = 67, because 67 is the 19th prime and the sum of the first 19 primes^2 = 24966 when divided by 19 equals 1314 which is an integer.

Mathematica

t = {}; sm = 0; Do[sm = sm + Prime[n]^2; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* T. D. Noe, Mar 19 2013 *)
k = 1; p = 2; s = 0; lst = {}; While[p < 1000000000, s = s + p^2; If[ Mod[s, k++] == 0, AppendTo[lst, p]]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Mar 08 2015 *)

Prog

(PARI) n=s=0; forprime(p=2, 1e9, if((s+=p^2)%n++==0, print1(p", "))) \\ Charles R Greathouse IV, Feb 06 2015

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, A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A030472 A106998 A275114 * A107214 A371509 A174602

Adjacent sequences: A217596 A217597 A217598 * A217600 A217601 A217602

Keyword

nonn,more

Author

Robert Price, Mar 19 2013

Extensions

a(13) from Willem Hengeveld, Nov 29 2020

a(14)-a(15) from Anders Kaseorg, Dec 02 2020

a(16) from Paul W. Dyson, Sep 03 2022

Status

approved