

A233576


Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^18.


1



1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 19, 21, 24, 27, 28, 36, 38, 41, 42, 45, 48, 54, 56, 57, 63, 69, 72, 74, 76, 84, 94, 107, 108, 112, 114, 126, 133, 135, 152, 168, 171, 189, 216, 228, 252, 266, 297, 312, 334, 336, 342, 360, 378, 380, 399, 423, 432, 441, 444
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(516) > 4*10^10.


LINKS

Robert Price, Table of n, a(n) for n = 1..515
OEIS Wiki, Sums of powers of primes divisibility sequences


EXAMPLE

a(5)=6 because 1 plus the sum of the first 6 primes^18 is 118016956494132483318 which is divisible by 6.


MATHEMATICA

p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^18; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)


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.
Sequence in context: A018772 A134003 A267301 * A128170 A018490 A113498
Adjacent sequences: A233573 A233574 A233575 * A233577 A233578 A233579


KEYWORD

nonn


AUTHOR

Robert Price, Dec 13 2013


STATUS

approved



