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 A125828 Numbers m that divide 2^8 + 3^8 + ... + prime(m)^8. 4

%I

%S 1,43,824747,3171671,767335408183,921649796621,1367268373487,

%T 8978321374181

%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(9) > 9*10^12. - _Bruce Garner_, Mar 30 2021

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>.

%F A125828 = 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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)