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A233768 Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^19. 0

%I

%S 1,2,4,5,6,10,12,53,226,361,400,620,935,1037,3832,3960,4956,7222,

%T 12183,13615,24437,80849,450827,680044,7388490,23503578,27723887,

%U 52048944,85860268,126177976,606788411,613917734,2693408896,3856356590,5167833600,5810025660,9197308014,10805855623,19751202045,19781610414,27240188169,30742119459

%N Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^19.

%C a(43) > 4*10^10.

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

%e a(5)=6 because 1 plus the sum of the first 6 primes^19 is 1523090798793695143992 which is divisible by 6.

%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^19; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

%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 _Robert Price_, Dec 15 2013

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)