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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 (list; graph; refs; listen; history; text; internal format)
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, ..., 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

REFERENCES

Matthijs Coster, Problem 2001/3-A of the Universitaire Wiskunde Competitie, Nieuw Arch. Wisk. 5/3 (2002), 92-94.

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, A094097-A094099.

Sequence in context: A138883 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

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Last modified August 28 03:16 EDT 2015. Contains 261112 sequences.