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

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

Offset

1,2

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

Table of n, a(n) for n=1..10.

OEIS Wiki, Sums of powers of primes divisibility sequences.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A212738 A291993 A228546 * A177417 A116139 A087529

Adjacent sequences: A125825 A125826 A125827 * A125829 A125830 A125831

Keyword

nonn,hard,more

Author

Alexander Adamchuk, Feb 03 2007

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

Status

approved