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Search: id:A060681
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| A060681 |
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Largest difference between consecutive divisors of n (ordered by size). |
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+0
8
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| 1, 2, 2, 4, 3, 6, 4, 6, 5, 10, 6, 12, 7, 10, 8, 16, 9, 18, 10, 14, 11, 22, 12, 20, 13, 18, 14, 28, 15, 30, 16, 22, 17, 28, 18, 36, 19, 26, 20, 40, 21, 42, 22, 30, 23, 46, 24, 42, 25, 34, 26, 52, 27, 44, 28, 38, 29, 58, 30, 60, 31, 42, 32, 52, 33, 66, 34, 46, 35, 70, 36, 72, 37
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Equivalently, a(n) = n - n/p, where p = A020639(n) is the smallest prime divisor of n.
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REFERENCES
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A. Balog, P. Erdos, and G. Tenenbaum, On Arithmetic Functions Involving Consecutive Divisors. In: Analytical Number Theory, pp. 77-90, Birkhauser, Basel, 1990.
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EXAMPLE
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For n=35, divisors={1,5,7,35}; differences={4,2,28}; a(35) = largest difference = 28 = 35 - 35/5.
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MATHEMATICA
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a[n_ ] := n-n/FactorInteger[n][[1, 1]]
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CROSSREFS
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Cf. A020639, A060680, A060682, A060683, A060685.
Sequence in context: A122376 A067240 A126080 this_sequence A060766 A029578 A054345
Adjacent sequences: A060678 A060679 A060680 this_sequence A060682 A060683 A060684
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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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