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A233264
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Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^12.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 24, 26, 27, 28, 30, 35, 36, 39, 40, 42, 45, 46, 48, 52, 54, 56, 60, 63, 65, 66, 70, 72, 78, 80, 84, 87, 90, 91, 100, 104, 105, 112, 117, 120, 126, 130, 138, 140, 144, 154, 156, 160, 168, 175, 176
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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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5 is a term because 1 plus the sum of the first 11 primes^12 is 3152514340085 which is divisible by 11.
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MAPLE
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MATHEMATICA
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p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^12; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
With[{nn=200}, Transpose[Select[Thread[{Accumulate[Prime[Range[nn]]^12], Range[nn]}], Divisible[#[[1]]+1, #[[2]]]&]][[2]]] (* Harvey P. Dale, May 28 2015 *)
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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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