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%I #11 Mar 17 2015 02:15:01
%S 2,2,2,3,2,4,2,2,2,3,3,2,5,2,6,2,2,3,3,4,2,7,3,5,2,8,2,2,4,2,2,2,2,4,
%T 4,2,9,2,3,3,3,6,2,10,2,2,5,4,5,3,7,2,11,2,12,2,2,6,2,2,2,3,2,3,4,3,8,
%U 4,6,5,5,2,13,3,9,3,3,3,2,14,2,2,7,4,7,2,15,2,3,5,3,10,5,6,2,16,2,2,8,2
%N Factors in factorizations of composite numbers into at least 2 factors >1.
%C Each factorization is given in nondecreasing order. To determine which of two factorizations a_1 * a_2 * ... * a_r and b_1 * ... * b_s (of the same number) comes first, find the smallest index k such that a_k != b_k. If k=r then the a-factorization comes first. If k=s the b-factorization comes first. Otherwise, if a_k < b_k then the a-factorization comes first; if b_k < a_k the b-factorization comes first.
%H Donald S. McDonald, <a href="http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=Pine.GSO.3.96.990207070038.14682A-100000%40atlantis">Posting to sci.math newsgroup, Feb 07 1999</a>
%e The first 20 terms come from the factorizations of 4, 6, 8, 9, 10 and 12: 4 = 2*2, 6 = 2*3, 8 = 2*4 = 2*2*2, 9 = 3*3, 10 = 2*5, 12 = 2*6 = 2*2*3=3*4.
%t mf[1, ds_] := {{}}; mf[n_, {}] := {}; mf[n_, ds_] := mf[n, ds]=If[Mod[n, ds[[1]]]==0, RotateRight[Join[Prepend[ #, ds[[1]]]&/@mf[n/ds[[1]], ds], RotateLeft[mf[n, Drop[ds, 1]]]]], mf[n, Drop[ds, 1]]]; mf[n_] := mf[n, Drop[Divisors[n], 1]]; Flatten[Drop[mf[ # ], 1]&/@Range[50]]
%Y Cf. A037025.
%K nonn
%O 1,1
%A _Donald S. McDonald_, Oct 26 2002
%E Edited by _Dean Hickerson_, Dec 06 2002
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