A232770 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer.

2, 83, 1979, 2081, 2326469, 6356923, 7170679, 63812027, 4652001719, 241949473277, 163220642765623, 1260677492111911, 8150959175977039

Offset: 1

Author

Robert Price, Nov 29 2013

Keywords

• nonn
• more

Comments

a(13) > 1352363608564489. - Bruce Garner, Aug 30 2021

a(14) > 18205684894350047. - Paul W. Dyson, Dec 06 2024

Examples

			a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 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]^13; 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)^13); s==0 \\ Charles R Greathouse IV, Nov 30 2013

Extensions

a(11) from Bruce Garner, Mar 23 2021

a(12) from Bruce Garner, Aug 30 2021

a(13) from Paul W. Dyson, Apr 20 2023