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

1,1

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

Links

Table of n, a(n) for n=1..10.

OEIS Wiki, Sums of powers of primes divisibility sequences

Formula

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

Example

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

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 *)

Prog

(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

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.

Sequence in context: A142890 A201183 A103404 * A230228 A197249 A151709

Adjacent sequences: A232819 A232820 A232821 * A232823 A232824 A232825

Keyword

nonn,more

Author

Robert Price, Nov 30 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

Status

approved