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Search: id:A060685
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| A060685 |
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Largest difference between consecutive divisors (ordered by size) of 2n+1. |
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+0
5
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| 2, 4, 6, 6, 10, 12, 10, 16, 18, 14, 22, 20, 18, 28, 30, 22, 28, 36, 26, 40, 42, 30, 46, 42, 34, 52, 44, 38, 58, 60, 42, 52, 66, 46, 70, 72, 50, 66, 78, 54, 82, 68, 58, 88, 78, 62, 76, 96, 66, 100, 102, 70, 106, 108, 74, 112, 92, 78, 102, 110, 82, 100, 126, 86, 130, 114
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Equivalently, a(2n+1) = 2n+1 - (2n+1)/p, where p = A020639(2n+1) is the smallest prime divisor of 2n+1.
The even case is trivial: for 2k the largest difference is k.
Successively greater values of a(n) occur when 2n+1 is prime.
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FORMULA
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A060681(2n+1)
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EXAMPLE
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For n=17, 2n+1=35; divisors={1,5,7,35}; differences={4,2,28}; a(17) = largest difference = 28 = 35 - 35/5.
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MATHEMATICA
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a[n_] := 2n+1-(2n+1)/FactorInteger[2n+1][[1, 1]]
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CROSSREFS
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Cf. A060681.
Sequence in context: A070229 A053568 A037225 this_sequence A073353 A066820 A087459
Adjacent sequences: A060682 A060683 A060684 this_sequence A060686 A060687 A060688
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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), Apr 19 2001
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 22 2002
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