A232733 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^6) / m is an integer.

2, 41647, 3197891, 630397289, 779089704751, 3819383648849, 44041722668737, 1322879640047263, 9863536132182127, 16069251644649407, 32520030920151967

Offset: 1

Author

Robert Price, Dec 02 2013

Keywords

• nonn
• more

Comments

The primes correspond to indices n = 1, 4357, 230065, 32826947, 29578097627 = A125825.

a(12) > 3.7*10^16. - Paul W. Dyson, Jan 17 2025

Examples

			a(2) = 41647, because 41647 is the 4357th prime and the sum of the first 4357 primes^6 = 2952411812082729747782733271068 when divided by 4357 equals 677624928180566845945084524 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]^6; 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)^6); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^6)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A125828(n)).

Extensions

a(6) from Bruce Garner, Jul 10 2021

a(7) from Paul W. Dyson, Jan 08 2021

a(8) from Bruce Garner, Jul 10 2021

a(9) from Paul W. Dyson, Oct 21 2022

a(10) from Paul W. Dyson, Oct 31 2022

a(11) from Paul W. Dyson, Dec 08 2022