A232822 Prime(m), where m is such that (Sum_{k=1..m} prime(k)^8) / m is an integer.

2, 191, 12599173, 53029063, 22806625723729, 27568116247823, 41455846079203, 289700908580893, 1194728983756489, 6275148480751847

Offset: 1

Author

Robert Price, Nov 30 2013

Keywords

• nonn
• more

Comments

The primes correspond to indices m = 1, 43, 824747, 3171671, ... = A125828. - M. F. Hasler, Dec 01 2013

a(10) > 1352363608564489. - Bruce Garner, Jul 07 2021

a(11) > 18205684894350047. - Paul W. Dyson, Dec 03 2024

Examples

			a(2) = 191, because 191 is the 43rd prime and the sum of the first 43 primes^8 = 7287989395992721002 = 43 * 169488125488202814.
		

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A125828.

Cf. A085450 (smallest m > 1 that 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]^8; 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)^8); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^8)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A125828(n)). - M. F. Hasler, Dec 01 2013

Extensions

a(5)-a(6) from Paul W. Dyson, Jan 01 2021

a(7) from Bruce Garner, Mar 02 2021

a(8) from Bruce Garner, Mar 30 2021

a(9) from Bruce Garner, Jul 07 2021

a(10) from Paul W. Dyson, Jul 07 2023