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 A233768 Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^19. 0
 1, 2, 4, 5, 6, 10, 12, 53, 226, 361, 400, 620, 935, 1037, 3832, 3960, 4956, 7222, 12183, 13615, 24437, 80849, 450827, 680044, 7388490, 23503578, 27723887, 52048944, 85860268, 126177976, 606788411, 613917734, 2693408896, 3856356590, 5167833600, 5810025660, 9197308014, 10805855623, 19751202045, 19781610414, 27240188169, 30742119459 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(43) > 4*10^10. LINKS EXAMPLE a(5)=6 because 1 plus the sum of the first 6 primes^19 is 1523090798793695143992 which is divisible by 6. MATHEMATICA 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 *) 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: A177911 A127092 A128171 * A240748 A171165 A039036 Adjacent sequences:  A233765 A233766 A233767 * A233769 A233770 A233771 KEYWORD nonn AUTHOR Robert Price, Dec 15 2013 STATUS approved

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