

A067957


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.


6



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
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OFFSET

1,3


COMMENTS

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, ..., n1, M1, n, M; for n odd: M+1, 1, M+2, 2, ..., M1, n1, M, n.  Daniel Asimov, May 04 2004


REFERENCES

Matthijs Coster, Problem 2001/3A of the Universitaire Wiskunde Competitie, Nieuw Arch. Wisk. 5/3 (2002), 9294.


LINKS

Table of n, a(n) for n=1..35.
Matthijs Coster, Sequences


EXAMPLE

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


CROSSREFS

Cf. A093313, A093314, A093315, A094097A094099.
Sequence in context: A257632 A107849 A053036 * A120326 A036406 A029007
Adjacent sequences: A067954 A067955 A067956 * A067958 A067959 A067960


KEYWORD

nonn


AUTHOR

Floor van Lamoen, Mar 06 2002


EXTENSIONS

a(31)a(35) from Jud McCranie, May 06 2004


STATUS

approved



