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A127643
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Composite numbers k that divide A123591(k) = ((2^k - 1)^(2^k) - 1)/(2^k)^2.
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2
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15, 51, 65, 85, 185, 221, 255, 341, 451, 533, 561, 595, 645, 679, 771, 1059, 1095, 1105, 1271, 1285, 1313, 1387, 1455, 1581, 1729, 1905, 2045, 2047, 2091, 2307, 2465, 2701, 2755, 2821, 2895, 3201, 3205, 3277, 3281, 3341, 3603, 3655, 3723, 3855, 4033, 4039
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OFFSET
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1,1
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COMMENTS
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p divides A123591(p) for prime p > 2.
Odd composite numbers k such that (2^k-1)^(2^k) == 1 (mod k). - Robert Israel, Jul 06 2017
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LINKS
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MAPLE
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select(n -> not isprime(n) and (2^n-1) &^ (2^n) mod n = 1, [seq(i, i=9..10000, 2)]); # Robert Israel, Jul 06 2017
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MATHEMATICA
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Do[f=PowerMod[(2^n-1), (2^n), n]-1; If[ !PrimeQ[n]&&IntegerQ[(n+1)/2]&&IntegerQ[f/n], Print[n]], {n, 2, 10000}]
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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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