A131264 Numbers k such that k divides 2^10 + 3^10 + 5^10 + ... + prime(k)^10.

1, 269, 41837, 36626159, 154578947, 2155054465, 19410890423, 30691222355, 247555091527, 2201220228533, 227735225320519, 478444326378215

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007

Keywords

• nonn
• more

Comments

a(11) > 2.6*10^12. - Bruce Garner, Mar 06 2021

a(13) > 5*10^14. - Paul W. Dyson, Dec 03 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]^10; If[ Mod[s, n] == 0, Print[n]], {n, 1000000}]

PARI

s=0;n=0;forprime(p=2, 1e9, s+=p^10; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011

Extensions

a(4) & a(5) from Robert G. Wilson v, Jun 28 2007

a(6)-a(9) from Charles R Greathouse IV, Apr 14 2011

a(10) from Bruce Garner, Mar 06 2021

a(11) from Paul W. Dyson, Jul 09 2023

a(12) from Paul W. Dyson, Dec 03 2024