A131272 Numbers k such that k divides Sum_{j=1..k} prime(j)^12.

1, 37, 7187, 3140407, 4986959, 5139161, 751213639, 163007938237, 5134788477263, 36197588005399, 940901369608517

Offset: 1

Author

Alexander Adamchuk, Jun 25 2007, Jun 28 2007

Keywords

• nonn

Comments

a(11) > 4*10^13. - Bruce Garner, Aug 30 2021

a(12) > 10^15. - Paul W. Dyson, Jan 04 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]^12; If[ Mod[s, n] == 0, Print[n]], {n, 1000000}]

PARI

s=0; n=0; forprime(p=2,1e9,s+=p^12; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011

Extensions

a(4)-a(6) from Robert G. Wilson v, Jun 30 2007

a(7)-a(8) from Charles R Greathouse IV, Apr 14 2011

a(9) from Bruce Garner, Mar 23 2021

a(10) from Bruce Garner, Aug 30 2021

a(11) from Paul W. Dyson, Jan 04 2024