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Search: id:A067957
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| A067957 |
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Number of divisor chains of length n: permutations s_1,s_2,...,s_n of 1,2,...,n such that for all j=1,2,...,n, s_j divides Sum_{i=1..j} s_i. |
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+0
7
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| 1, 1, 2, 2, 4, 5, 7, 7, 24, 22, 29, 39, 67, 55, 386, 235, 312, 347, 451, 1319, 5320, 3220, 4489, 20237, 36580, 52875, 197103, 216562, 289478, 567396, 659647, 1111153, 3131774, 2200426, 29523302
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Apparently this sequence originated in a problem composed by Matthijs Coster in 2002.
Let M = floor(n/2), then the following permutations always work: for n even: M+1, 1, M+2, 2, ..., n-1, M-1, n, M; for n odd: M+1, 1, M+2, 2, ..., M-1, n-1, M, n. - Daniel Asimov, May 04 2004
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REFERENCES
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Matthijs Coster, Problem 2001/3-A of the Universitaire Wiskunde Competitie, Nieuw Arch. Wisk. 5/3 (2002), 92-94.
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LINKS
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Matthijs Coster, Sequences
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EXAMPLE
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Examples of divisor chains of lengths 1 through 9:
1
2 1
3 1 2
4 2 3 1
5 1 2 4 3
6 2 4 3 5 1
7 1 2 5 3 6 4
8 2 5 3 6 4 7 1
8 4 3 5 1 7 2 6 9
The five divisor chains of length 6 are:
4 1 5 2 6 3
4 2 6 3 5 1
5 1 2 4 6 3
5 1 6 4 2 3
6 2 4 3 5 1. - Eugene McDonnell, May 21, 2004
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CROSSREFS
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Cf. A093313, A093314, A093315, A094097-A094099.
Sequence in context: A138883 A107849 A053036 this_sequence A120326 A036406 A029007
Adjacent sequences: A067954 A067955 A067956 this_sequence A067958 A067959 A067960
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KEYWORD
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nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Mar 06 2002
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EXTENSIONS
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a(31)-a(35) from Jud McCranie (j.mccranie(AT)comcast.net), May 06 2004
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