Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #25 May 12 2024 06:47:46
%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 1111153,3131774,2200426,29523302,34214028,48161995,32616148,242860900,293579041,363415618
%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
%E a(36)-a(41) from _Zhao Hui Du_, May 12 2024