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A232823
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Numbers k such that k divides 1 + Sum_{j=1..k} (prime(j)^8).
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1
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1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 24, 28, 30, 32, 37, 39, 40, 45, 48, 60, 64, 80, 90, 96, 100, 104, 120, 133, 160, 168, 174, 180, 205, 211, 240, 247, 320, 360, 456, 480, 512, 540, 560, 563, 580, 676, 692, 735, 820, 864, 930, 960, 1215, 1216, 1368
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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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a(7)=8 because 1 plus the sum of the first 8 primes^8 is 24995572328 which is divisible by 8.
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MATHEMATICA
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p = 2; k = 0; s = 1; lst = {}; While[k < 521330000, s = s + p^8; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p](* Derived from A128169 *)
With[{nn=1400}, Select[Thread[{Range[nn], Accumulate[Prime[Range[nn]]^8]+1}], Mod[ #[[2]], #[[1]]] == 0&]][[;; , 1]] (* Harvey P. Dale, Jul 20 2024 *)
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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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