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A330382
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Composite numbers k such that k-1 divides 2^k-2.
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1
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55, 295, 343, 1027, 1135, 1315, 1807, 2059, 2395, 3403, 4375, 5335, 6175, 6499, 7183, 7939, 9235, 10207, 12643, 13123, 14155, 16003, 16255, 19495, 21547, 23815, 27595, 27703, 30619, 35479, 37927, 43219, 45487, 48007, 48763, 50275, 55567, 58483, 64387, 64639, 74899
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OFFSET
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1,1
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COMMENTS
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If k is in this sequence, then 2^k-1 is also a term, so this sequence is infinite.
Also 2^p-1 is in this sequence for such prime p in A069051 that 2^p-1 is composite.
Theorem: if k-1 | 2^k-2, then m-1 | 2^m-2, where m = 2^k-1.
It seems that A007013(n)^3 for n > 1 and A007013(n) for n > 4 are in this sequence.
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LINKS
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MATHEMATICA
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Select[Range[75000], CompositeQ[#] && Divisible[PowerMod[2, #, # - 1] - 2, # - 1] &]
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PROG
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(PARI) forcomposite(k=1, 75000, if(!((2^k-2)%(k-1)), print1(k, ", "))) \\ Hugo Pfoertner, Dec 12 2019
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CROSSREFS
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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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