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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

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)