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

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

Offset: 1

Author

Alexander Adamchuk, Feb 03 2007

Keywords

• hard
• nonn

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

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences.

Crossrefs

Cf. A232865.

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

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