Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #46 Dec 03 2024 08:14:51
%S 1,43,824747,3171671,767335408183,921649796621,1367268373487,
%T 8978321374181,35467651791527,177538435814203
%N Numbers m that divide 2^8 + 3^8 + ... + prime(m)^8.
%C No other terms up to 10^8. - _Stefan Steinerberger_, Jun 06 2007
%C No other terms up to pi(10^13). - _Charles R Greathouse IV_, Apr 14 2011
%C a(10) > 4*10^13. - _Bruce Garner_, Jul 07 2021
%C a(11) > 5*10^14. - _Paul W. Dyson_, Dec 03 2024
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>.
%F Equals A000720 o A232822, i.e., a(n)=PrimePi(A232822(n)). - _M. F. Hasler_, Dec 01 2013
%t s = 0; t = {}; Do[s = s + Prime[n]^8; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t
%o (PARI) S=n=0; forprime(p=1,,(S+=p^8)%n++||print1(n",")) \\ _M. F. Hasler_, Dec 01 2013
%K nonn,hard,more
%O 1,2
%A _Alexander Adamchuk_, Feb 03 2007
%E a(4) from _Stefan Steinerberger_, Jun 06 2007
%E a(5)-a(6) from _Paul W. Dyson_, Jan 01 2021
%E a(7) from _Bruce Garner_, Mar 02 2021
%E a(8) from _Bruce Garner_, Mar 30 2021
%E a(9) from _Bruce Garner_, Jul 07 2021
%E a(10) from _Paul W. Dyson_, Jul 07 2023