A232865 Primes p such that the average of the seventh power of primes up to p is an integer.

2, 97, 14293, 247997, 7979737, 15749303, 344468591, 25934255929, 40224745543, 16495569405383, 53941465463489, 84897825837611, 244949151647509, 757938163218799, 1594375071689591, 1674528348898463, 5347819657753523, 6152744788157173, 47008163075851819

Offset: 1

Author

M. F. Hasler, Dec 01 2013

Keywords

• nonn
• more
• hard

Comments

Otherwise said, prime(m) such that m divides prime(1)^7 + ... + prime(m)^7.

a(17) > 1877564517734839. - Bruce Garner, Aug 30 2021

a(18) > 5493145969370039. - Paul W. Dyson, Mar 02 2022

a(19) > 6728882502496787. - Bruce Garner, Sep 18 2022

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

PARI

S=n=0;forprime(p=1,,(S+=p^7)%n++||print1(p","))

Formula

a(n) = prime(A125826(n)).

Extensions

a(10) from Paul W. Dyson, Jan 05 2021

a(11)-a(12) from Bruce Garner, Feb 26 2021

a(13) from Bruce Garner, Mar 23 2021

a(14) from Bruce Garner, May 19 2021

a(15)-a(16) from Bruce Garner, Aug 30 2021

a(17) from Paul W. Dyson, Mar 02 2022

a(18) from Bruce Garner, Sep 18 2022

a(19) from Paul W. Dyson, Jan 17 2024