A125827 Numbers m that divide 2^11 + 3^11 + 5^11 + ... + prime(m)^11.

1, 25, 59, 2599, 6195, 421407, 11651191, 19293221, 255136097, 1820015683, 2183556659, 7993872143, 9850779563, 2006892138335, 2649677145789, 6645858099781, 318039538085101, 414996765110825

Offset: 1

Author

Alexander Adamchuk, Feb 03 2007

Keywords

• hard
• more
• nonn

Comments

a(17) > 8*10^12. - Bruce Garner, Mar 29 2021

a(19) > 5*10^14. - Paul W. Dyson, Dec 31 2024

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

Mathematica

s = 0; Do[s = s + Prime[n]^11; If[ Mod[s, n] == 0, Print[n]], {n, 7000}]

PARI

s=0; n=0; forprime(p=2, 4e9, s+=p^11; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 20 2011

Extensions

3 more terms from Stefan Steinerberger, Jun 06 2007

1 more term from Sean A. Irvine, Jan 26 2011

a(10)-a(13) from Charles R Greathouse IV, Mar 20 2011

a(14) from Paul W. Dyson, Jan 08 2021

a(15) from Bruce Garner, Mar 08 2021

a(16) from Bruce Garner, Mar 29 2021

a(17) from Paul W. Dyson, Jan 03 2023

a(18) from Paul W. Dyson, Dec 20 2024