A125907 Numbers k such that k divides 2^4 + 3^4 + 5^4 + ... + prime(k)^4.

1, 2951, 38266951, 3053263643573, 3798632877308897

Offset: 1

Author

Alexander Adamchuk, Feb 04 2007

Keywords

• bref
• hard
• more
• nonn

Comments

No more terms to 10^13. - Charles R Greathouse IV, Mar 21 2011

a(4) is less than 10^13 contradicting the previous comment. It was found using the primesieve library by Kim Walisch and gmplib. - Bruce Garner, Feb 26 2021

a(6) > 4*10^15. - Paul W. Dyson, Nov 19 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.

Cf. A122102, A232869, A128168, A233893.

Programs

Mathematica

a(1) = 1; s = 2^4; Do[s = s + Prime[2n]^4+Prime[2n+1]^4; If[ Mod[s, 2n+1] == 0, Print[2n+1]], {n,1, 20000000}]

PARI

s=0; n=0; forprime(p=2, 4e9, s+=p^4; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 21 2011

Extensions

a(4) from Bruce Garner, Feb 26 2021

a(5) from Paul W. Dyson, May 09 2024