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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. 8

%I #13 Feb 05 2019 14:21:47

%S 1,1,1,2,2,4,5,7,7,24,22,29,39,67,55,386,235,312,347,451,1319,5320,

%T 3220,4489,20237,36580,52875,197103,216562,289478,567396,659647,

%U 1111153,3131774,2200426,29523302

%N 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.

%C Apparently this sequence originated in a problem composed by Matthijs Coster in 2002.

%C 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

%H Matthijs Coster, <a href="http://www.coster.demon.nl/sequences/index.html">Sequences</a>

%H Matthijs Coster, <a href="http://www.nieuwarchief.nl/serie5/pdf/naw5-2002-03-1-092.pdf">Problem 2001/3-A of the Universitaire Wiskunde Competitie</a>, Nieuw Arch. Wisk. 5/3 (2002), 92-94.

%e Examples of divisor chains of lengths 1 through 9:

%e 1

%e 2 1

%e 3 1 2

%e 4 2 3 1

%e 5 1 2 4 3

%e 6 2 4 3 5 1

%e 7 1 2 5 3 6 4

%e 8 2 5 3 6 4 7 1

%e 8 4 3 5 1 7 2 6 9

%e The five divisor chains of length 6 are:

%e 4 1 5 2 6 3

%e 4 2 6 3 5 1

%e 5 1 2 4 6 3

%e 5 1 6 4 2 3

%e 6 2 4 3 5 1. - Eugene McDonnell, May 21 2004

%Y Cf. A093313, A093314, A093315, A094097, A094098, A094099.

%K nonn

%O 0,4

%A _Floor van Lamoen_, Mar 06 2002

%E a(31)-a(35) from _Jud McCranie_, May 06 2004

%E a(0)=1 prepended by _Alois P. Heinz_, Aug 26 2017

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)