cp's OEIS Frontend

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.

%I A067957 #25 May 12 2024 06:47:46
%S A067957 1,1,1,2,2,4,5,7,7,24,22,29,39,67,55,386,235,312,347,451,1319,5320,
%T A067957 3220,4489,20237,36580,52875,197103,216562,289478,567396,659647,
%U A067957 1111153,3131774,2200426,29523302,34214028,48161995,32616148,242860900,293579041,363415618
%N 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.
%C A067957 Apparently this sequence originated in a problem composed by Matthijs Coster in 2002.
%C A067957 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 A067957 Matthijs Coster, <a href="http://www.coster.demon.nl/sequences/index.html">Sequences</a>
%H A067957 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 A067957 Examples of divisor chains of lengths 1 through 9:
%e A067957   1
%e A067957   2 1
%e A067957   3 1 2
%e A067957   4 2 3 1
%e A067957   5 1 2 4 3
%e A067957   6 2 4 3 5 1
%e A067957   7 1 2 5 3 6 4
%e A067957   8 2 5 3 6 4 7 1
%e A067957   8 4 3 5 1 7 2 6 9
%e A067957 The five divisor chains of length 6 are:
%e A067957   4 1 5 2 6 3
%e A067957   4 2 6 3 5 1
%e A067957   5 1 2 4 6 3
%e A067957   5 1 6 4 2 3
%e A067957   6 2 4 3 5 1. - Eugene McDonnell, May 21 2004
%Y A067957 Cf. A093313, A093314, A093315, A094097, A094098, A094099.
%K A067957 nonn
%O A067957 0,4
%A A067957 _Floor van Lamoen_, Mar 06 2002
%E A067957 a(31)-a(35) from _Jud McCranie_, May 06 2004
%E A067957 a(0)=1 prepended by _Alois P. Heinz_, Aug 26 2017
%E A067957 a(36)-a(41) from _Zhao Hui Du_, May 12 2024