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

1,1

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

Links

Table of n, a(n) for n=1..11.

OEIS Wiki, Sums of powers of primes divisibility sequences

Formula

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

Example

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.

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 *)

Prog

(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

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.

Sequence in context: A257968 A303738 A055578 * A106025 A157959 A364134

Adjacent sequences: A232730 A232731 A232732 * A232734 A232735 A232736

Keyword

nonn,more

Author

Robert Price, Dec 02 2013

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

Status

approved