A128170 - OEIS

%I #32 Apr 07 2021 20:40:15

%S 1,2,3,4,6,7,8,9,12,14,18,21,24,27,28,29,34,36,42,45,48,54,56,63,72,

%T 84,112,126,159,168,174,198,204,216,252,310,312,336,360,400,408,441,

%U 504,505,540,588,591,657,672,716,864,900,1080,1152,1316,1350,1380,1680,1722

%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^6.

%C a(301) > 1.4*10^13. - _Bruce Garner_, Apr 07 2021

%H Bruce Garner, <a href="/A128170/b128170.txt">Table of n, a(n) for n = 1..300</a> (first 229 terms from Robert Price)

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

%t s = 1; Do[s = s + Prime[n]^6; If[ Mod[s, n] == 0, Print[n]], {n, 10000}]

%t Module[{nn=1750,pr},pr=Accumulate[Prime[Range[nn]]^6];Select[Thread[ {Range[ nn],pr}],Divisible[#[[2]]+1,#[[1]]]&]][[All,1]] (* _Harvey P. Dale_, Feb 10 2019 *)

%o (PARI) n=0; s=1; forprime(p=2,,s+=p^6; if(s%n++==0, print1(n", "))) \\ _Charles R Greathouse IV_, Dec 03 2013

%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 nonn

%O 1,2

%A _Alexander Adamchuk_, Feb 22 2007