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Search: id:A066637
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| A066637 |
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Total number of elements in all factorizations of n with all factors >1. |
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+0
2
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| 0, 1, 1, 3, 1, 3, 1, 6, 3, 3, 1, 8, 1, 3, 3, 12, 1, 8, 1, 8, 3, 3, 1, 17, 3, 3, 6, 8, 1, 10, 1, 20, 3, 3, 3, 22, 1, 3, 3, 17, 1, 10, 1, 8, 8, 3, 1, 34, 3, 8, 3, 8, 1, 17, 3, 17, 3, 3, 1, 27, 1, 3, 8, 35, 3, 10, 1, 8, 3, 10, 1, 46, 1, 3, 8, 8, 3, 10, 1, 34, 12, 3, 1, 27, 3, 3, 3, 17, 1, 27, 3, 8, 3, 3, 3
(list; graph; listen)
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OFFSET
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1,4
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REFERENCES
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Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
Amarnath Murthy, Length and extent of Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
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EXAMPLE
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a(12) = 8: there are 4 factorizations of 12: (12), (6*2), (4*3), (3*3*2) having 1, 2, 2, 3 elements respectively, a total of 8.
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MATHEMATICA
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g[1, r_] := g[1, r]={1, 0}; g[n_, r_] := g[n, r]=Module[{ds, i, val}, ds=Select[Divisors[n], 1<#<=r&]; val={0, 0}+Sum[g[n/ds[[i]], ds[[i]]], {i, 1, Length[ds]}]; val+{0, val[[1]]}]; a[n_] := g[n, n][[2]]; a/@Range[95] (* g[n, r] = {c, f}, where c is the number of factorizations of n with factors <= r and f is the total number of factors in them. - Dean Hickerson Oct 28 2002 *)
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CROSSREFS
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Sequence in context: A103790 A013603 A126212 this_sequence A050336 A095250 A135521
Adjacent sequences: A066634 A066635 A066636 this_sequence A066638 A066639 A066640
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 28 2001
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