A125828 Numbers m that divide 2^8 + 3^8 + ... + prime(m)^8.

1, 43, 824747, 3171671, 767335408183, 921649796621, 1367268373487, 8978321374181, 35467651791527, 177538435814203

Offset: 1

Author

Alexander Adamchuk, Feb 03 2007

Keywords

• nonn
• hard
• more

Comments

No other terms up to 10^8. - Stefan Steinerberger, Jun 06 2007

No other terms up to pi(10^13). - Charles R Greathouse IV, Apr 14 2011

a(10) > 4*10^13. - Bruce Garner, Jul 07 2021

a(11) > 5*10^14. - Paul W. Dyson, Dec 03 2024

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences.

Programs

Mathematica

s = 0; t = {}; Do[s = s + Prime[n]^8; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t

PARI

S=n=0; forprime(p=1,,(S+=p^8)%n++||print1(n",")) \\ M. F. Hasler, Dec 01 2013

Formula

Equals A000720 o A232822, i.e., a(n)=PrimePi(A232822(n)). - M. F. Hasler, Dec 01 2013

Extensions

a(4) from Stefan Steinerberger, Jun 06 2007

a(5)-a(6) from Paul W. Dyson, Jan 01 2021

a(7) from Bruce Garner, Mar 02 2021

a(8) from Bruce Garner, Mar 30 2021

a(9) from Bruce Garner, Jul 07 2021

a(10) from Paul W. Dyson, Jul 07 2023