A131275 - OEIS

%I #36 Apr 19 2024 02:28:05

%S 1,17,25,31,1495,5555,8185,8647,106841,187329,345377,1811351,2179119,

%T 2863775,6368703,10250821,59137893,337430815,11349203711,183233304195,

%U 12538656829431,40154010310477,1761333303516473

%N Numbers k such that k divides Sum_{j=1..k} prime(j)^15.

%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]^15; If[ Mod[s, n] == 0, Print[n]], {n, 400000}]

%t With[{nn = 3*10^6},Select[Thread[{Accumulate[Prime[ Range[nn]]^15],Range[ nn]}],Divisible[#[[1]], #[[2]]] &]][[All, 2]] (* This will generate the first 14 terms of the sequence; to generate more, increase the value of nn, but it may take a long time to run. *) (* _Harvey P. Dale_, Oct 03 2016 *)

%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(12)-a(17) from _Robert G. Wilson v_, Jul 02 2007

%E a(18)-a(19) from _Robert Price_, Dec 09 2013

%E a(20) from _Karl-Heinz Hofmann_, Feb 17 2021

%E a(21) from _Bruce Garner_, Apr 30 2021

%E a(22) from _Bruce Garner_, Jan 07 2022

%E a(23) from _Paul W. Dyson_, Apr 18 2024