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A127104
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Numbers k such that k^2 divides 4^k-1.
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28
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1, 3, 21, 903, 2667, 7077, 113799, 114681, 304311, 389193, 898779, 932799, 4893357, 6099429, 8131683, 8776257, 14452473, 38350263, 38647497, 40647747, 49427511, 99583113, 118465473, 128794323, 131158041, 152643813, 262275447, 300510651, 314353263, 335873559, 349662369
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OFFSET
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1,2
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COMMENTS
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3 divides a(n) for n > 1.
7 divides a(n) for n > 2.
43 divides a(n) for n = {4, 8, 9, 10, 12, 13, 16, ...}.
127 divides a(n) for n = {5, 8, 11, 14, 15, 17, ...}.
Prime factors of a(n) in order of their appearance in {a(n)} are {3, 7, 43, 127, 337, 5419, 431, 1033, 5419, 2287, 3049, 9719, ...}. (End)
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LINKS
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MATHEMATICA
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Select[Range[30000], IntegerQ[(PowerMod[4, #, #^2 ]-1)/#^2 ]&]
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PROG
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(PARI) is(k) = Mod(4, k^2)^k == 1; \\ Amiram Eldar, May 25 2024
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CROSSREFS
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Subset of A014945 (numbers k such that k divides 4^nk-1).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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