A131276 - OEIS

%I #23 Mar 29 2021 15:18:29

%S 1,3131,6289,323807,443371,83802527023,4076111200313

%N Numbers m such that m divides Sum_{k=1..m} prime(k)^16.

%C a(7) > 10^11. - _Paul W. Dyson_, Dec 30 2020

%C a(8) > 4.1*10^12. - _Bruce Garner_, Mar 24 2021

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

%t s = 0; Do[s = s + Prime[n]^16; If[ Mod[s, n] == 0, Print[n]], {n, 500000}]

%t Transpose[Select[With[{nn=500000},Thread[{Range[nn],Accumulate[ Prime[ Range[nn]]^16]}]], Divisible[ #[[2]],#[[1]]]&]][[1]]

%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

%K more,nonn,less

%O 1,2

%A _Alexander Adamchuk_, Jun 25 2007

%E a(6) from _Paul W. Dyson_, Dec 30 2020

%E a(7) from _Bruce Garner_, Mar 24 2021