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Search: id:A097406
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| A097406 |
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Largest primitive prime factor of 2^n-1. |
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+0
3
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| 0, 3, 7, 5, 31, 0, 127, 17, 73, 11, 89, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41, 337, 683, 178481, 241, 1801, 2731, 262657, 113, 2089, 331, 2147483647, 65537, 599479, 43691, 122921, 109, 616318177, 174763, 121369, 61681, 164511353, 5419
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Except for a(6) where 2^6-1 = 1*63; 3*21; 7*9. 9, 21 and 63 are composite.
Prime factors 3 & 7 first appear when n=2 & n=3 so neither of them is unique.
Conjectures: (1) For every n the highest unique prime factor is of the form kn+1. The values for k are in A097407. (2) For each composite n many factors of the form kn+1 occur intermittently but always singly in any cofactor pair. (3) For each prime n every factor is of the form kn+1.
A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 for any r<n, cf. A086251.
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CROSSREFS
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Cf. A064078, A097407.
Sequence in context: A115765 A112071 A046561 this_sequence A112927 A064078 A048857
Adjacent sequences: A097403 A097404 A097405 this_sequence A097407 A097408 A097409
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KEYWORD
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nonn,easy
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AUTHOR
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Marco Matosic (marcomatosic(AT)hotmail.com), Aug 16 2004
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EXTENSIONS
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More terms and better description from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 03 2004
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