A128170 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^6.

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, 84, 112, 126, 159, 168, 174, 198, 204, 216, 252, 310, 312, 336, 360, 400, 408, 441, 504, 505, 540, 588, 591, 657, 672, 716, 864, 900, 1080, 1152, 1316, 1350, 1380, 1680, 1722

Offset: 1

Author

Alexander Adamchuk, Feb 22 2007

Keywords

• nonn

Comments

a(301) > 1.4*10^13. - Bruce Garner, Apr 07 2021

Links

• Bruce Garner, Table of n, a(n) for n = 1..300 (first 229 terms from Robert Price)
• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

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

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

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

Programs

Mathematica

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

PARI

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