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A060682
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Number of distinct differences between consecutive divisors of n (ordered by size).
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5
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1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 3, 1, 4, 3, 3, 1, 4, 2, 3, 3, 5, 1, 5, 1, 5, 3, 3, 3, 5, 1, 3, 3, 5, 1, 4, 1, 5, 4, 3, 1, 5, 2, 5, 3, 5, 1, 4, 3, 6, 3, 3, 1, 7, 1, 3, 4, 6, 3, 5, 1, 5, 3, 6, 1, 6, 1, 3, 3, 5, 3, 5, 1, 7, 4, 3, 1, 6, 3, 3, 3, 7, 1, 7, 2, 5, 3, 3, 3, 6, 1, 5, 4, 6, 1, 5, 1, 7, 5, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| Number of all differences for n is d(n)-1 = A000005(n)-1. Increments are not necessarily different, so a(n)<=d(n)-1.
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REFERENCES
| 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
| For n=70, divisors={1,2,5,7,10,14,35,70}; differences={1,3,2,3,4,21,35}; a(70) = number of distinct differences = 6.
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MATHEMATICA
| a[n_ ] := Length[Union[Drop[d=Divisors[n], 1]-Drop[d, -1]]]
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CROSSREFS
| Cf. A000005, A060680, A060681, A060683.
Sequence in context: A173442 A112309 A160006 * A093873 A161148 A143773
Adjacent sequences: A060679 A060680 A060681 * A060683 A060684 A060685
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Apr 19 2001
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 22 2002
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