cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A232869 Primes p such that the average of the fourth powers of primes up to p is an integer.

Original entry on oeis.org

2, 26893, 741080929, 95114243761787, 146234140655742407
Offset: 1

Views

Author

M. F. Hasler, Dec 01 2013

Keywords

Comments

Otherwise said, prime(n) such that n divides prime(1)^4 + ... + prime(n)^4. The n-values (indices) are given in A125907.

Crossrefs

Cf. A171399, A111441, A217599 (analog for squares), A223936 (3rd powers), A224083 (5th powers), A232733 (6th powers), A232865 (7th powers), A232822 (8th powers), A232962 (9th powers), A233132 (10th powers).

Programs

  • PARI
    S=n=0;forprime(p=1,,(S+=p^4)%n++||print1(p","))

Formula

a(n) = prime(A125907(n)).

Extensions

a(4) from Bruce Garner, Feb 27 2021
a(5) from Paul W. Dyson, May 09 2024

A125826 Numbers m that divide 2^7 + 3^7 + 5^7 + ... + prime(m)^7.

Original entry on oeis.org

1, 25, 1677, 21875, 538513, 1015989, 18522325, 1130976595, 1721158369, 561122374231, 1763726985077, 2735295422833, 7631117283951, 22809199833151, 46929434362563, 49217568518075, 151990420653423, 174172511353413, 1258223430425543
Offset: 1

Views

Author

Alexander Adamchuk, Feb 03 2007

Keywords

Comments

See A232865 for prime(a(n)). - M. F. Hasler, Dec 01 2013
a(17) > 5.5*10^13. - Bruce Garner, Aug 30 2021
a(18) > 1.56*10^14. - Paul W. Dyson, Mar 02 2022
a(19) > 1.9*10^14. - Bruce Garner, Sep 18 2022

Crossrefs

Cf. A232865.
Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Programs

  • Mathematica
    s = 0; Do[s = s + Prime[n]^7; If[ Mod[s, n] == 0, Print[n]], {n, 25000}]
  • PARI
    s=0; n=0; forprime(p=2, 4e9, s+=p^7; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 16 2011

Extensions

More terms from Ryan Propper, Mar 26 2007
a(8)-a(9) from Charles R Greathouse IV, Mar 16 2011
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
Showing 1-2 of 2 results.