A131263 Numbers k such that k divides 2^9 + 3^9 + 5^9 + ... + prime(k)^9.

1, 281525, 1011881, 13721649, 309777093, 417800903, 12252701193, 27377813605, 37762351523, 245773819141, 51230573255953, 82578361848569, 277900491430385

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007, Jun 27 2007

Keywords

• nonn
• more

Comments

a(12) > 5.5*10^13. - Paul W. Dyson, Mar 27 2021

a(13) > 10^14. - Bruce Garner, Jan 10 2022

a(14) > 3*10^14. - Paul W. Dyson, Aug 11 2022

a(14) > 5*10^14. - Paul W. Dyson, Dec 16 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]^9; If[ Mod[s, n] == 0, Print[n]], {n, 1100000}]

PARI

s=0; n=0; forprime(p=2, 1e9, s+=p^9; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011

Extensions

a(4) from Robert G. Wilson v, Jun 27 2007

a(5)-a(10) from Charles R Greathouse IV, Apr 14 2011

a(11) from Paul W. Dyson, Mar 27 2021

a(12) from Bruce Garner, Jan 10 2022

a(13) from Paul W. Dyson, Aug 11 2022