login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (fvlamoen(AT)hotmail.com), Mar 06 2002

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 01:41 EST 2014. Contains 250286 sequences.