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A076716
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Number of distinct factorizations of n! with all factors >1.
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1
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1, 1, 2, 7, 21, 98, 392, 2116, 11830, 70520, 425240, 2787810, 19530213, 144890639, 1149978830, 8558078111, 76417516719, 618437486332, 6087770992601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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EXAMPLE
| a(3)=2 because 3!= 6 = 2.3 has just 2 factorizations. 4!= 24 = 2.12 =2.2.6 = 2.2.2.3 = 2.3.4 = 3.8 = 4.6 has 7 factorizations.
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MATHEMATICA
| c[1, r_] := c[1, r]=1; c[n_, r_] := c[n, r]=Module[{ds, i}, ds=Select[Divisors[n], 1<#<=r&]; Sum[c[n/ds[[i]], ds[[i]]], {i, 1, Length[ds]}]]; a[n_] := c[n!, n! ]; a/@Range[16] (* c[n, r] is the number of factorizations of n with factors <= r. - Dean Hickerson Oct 29 2002 *)
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CROSSREFS
| Cf. A001055.
Sequence in context: A150319 A150320 A150321 * A088591 A175871 A137107
Adjacent sequences: A076713 A076714 A076715 * A076717 A076718 A076719
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KEYWORD
| nonn,more
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AUTHOR
| Donald S. McDonald (don.mcdonald(AT)paradise.net.nz), Oct 27 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 29 2002
4 more terms from Ryan Propper (rpropper(AT)stanford.edu), May 20 2007
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