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A076709
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Factors in factorizations of composite numbers into at least 2 factors >1.
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1
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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LINKS
| Donald S. McDonald, Posting to sci.math newsgroup, Feb 07 1999
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EXAMPLE
| 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
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MATHEMATICA
| 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]]
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CROSSREFS
| Cf. A037025.
Sequence in context: A092964 A183368 A156862 * A110021 A036013 A126336
Adjacent sequences: A076706 A076707 A076708 * A076710 A076711 A076712
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KEYWORD
| nonn
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AUTHOR
| Donald S. McDonald (don.mcdonald(AT)paradise.net.nz), Oct 26 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 06 2002
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