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A233768
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Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^19.
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1
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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6 is a term because 1 plus the sum of the first 6 primes^19 is 1523090798793695143992 which is divisible by 6.
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MATHEMATICA
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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 *)
Module[{nn=74*10^5, apr}, apr=Accumulate[Prime[Range[nn]]^19]; Select[Range[ nn], Divisible[1+apr[[#]], #]&]] (* The program generates the first 25 terms of the sequence. To generate more, increase the value of nn, but the program may take a long time to run. *) (* Harvey P. Dale, Oct 02 2021 *)
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CROSSREFS
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Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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