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Search: id:A049094
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| A049094 |
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2^n - 1 is divisible by a square. |
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+0
2
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| 6, 12, 18, 20, 21, 24, 30, 36, 40, 42, 48, 54, 60, 63, 66, 72, 78, 80, 84, 90, 96, 100, 102, 105, 108, 110, 114, 120, 126, 132, 136, 138, 140, 144, 147, 150, 155, 156, 160, 162, 168, 174, 180, 186, 189, 192, 198, 200, 204, 210, 216, 220, 222, 228, 231, 234, 240
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: 2^n-1 is square-free iff gcd(n,2^n-1)=1. If true the conjecture would imply that Mersenne numbers (cf. A001348) are square-free. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 12 2002. But the conjecture is not true: counterexamples are n = 364 and n = 1755, i.e. gcd(364,2^364-1) = 1 and (2^364-1) mod 1093^2 = 0 and gcd(1755,2^1755-1) = 1 and (2^1755-1) mod 3511^2 = 0, cf. A001220. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 01 2005
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, A3.
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LINKS
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Andy Steward, Factorizations of Generalized Repunits
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EXAMPLE
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a[ 2 ]=12 because 2^12-1=4095=5*(3^2)*7*13 is divisible by a square
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CROSSREFS
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Cf. A014491, A049093, A049096, A049095.
Cf. A001220.
Sequence in context: A046626 A023495 A037363 this_sequence A105289 A051774 A119357
Adjacent sequences: A049091 A049092 A049093 this_sequence A049095 A049096 A049097
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 12 2002
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