A232822 -id:A232822 - cp's OEIS frontend

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

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

Offset: 1

Alexander Adamchuk, Feb 03 2007

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

OEIS Wiki, Sums of powers of primes divisibility sequences.

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

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

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

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

A232869 Primes p such that the average of the fourth powers of primes up to p is an integer.

Original entry on oeis.org

2, 26893, 741080929, 95114243761787, 146234140655742407

Offset: 1

M. F. Hasler, Dec 01 2013

Otherwise said, prime(n) such that n divides prime(1)^4 + ... + prime(n)^4. The n-values (indices) are given in A125907.

Cf. A171399, A111441, A217599 (analog for squares), A223936 (3rd powers), A224083 (5th powers), A232733 (6th powers), A232865 (7th powers), A232822 (8th powers), A232962 (9th powers), A233132 (10th powers).

S=n=0;forprime(p=1,,(S+=p^4)%n++||print1(p","))

a(n) = prime(A125907(n)).

a(4) from Bruce Garner, Feb 27 2021

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

cp's OEIS Frontend

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

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