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Search: id:A116900
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| A116900 |
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Number of partitions of n into at least two parts such that the product of largest and smallest part is equal to n. |
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+0
3
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| 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 1, 5, 0, 7, 0, 7, 4, 8, 0, 21, 1, 14, 13, 25, 0, 43, 0, 44, 31, 41, 2, 121, 0, 66, 73, 126, 0, 215, 0, 193, 179, 165, 0, 554, 1, 285, 346, 491, 0, 890, 65, 772, 704, 574, 0, 2330, 0, 847, 1392, 1828, 254, 3212, 0, 2754, 2649, 2282, 0, 7907
(list; graph; listen)
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OFFSET
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1,12
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COMMENT
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Clearly a(p)=0, when p is prime.
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FORMULA
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a(n) = coefficient of x^n in expansion of Sum_{d|n} x^(d+n/d)/Product(1-x^k,k=d..n/d). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Nov 24 2008]
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EXAMPLE
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a(21)=4 since property holds for 4 partitions of 21: (7,7,4,3), (7,6,5,3), (7,5,3,3,3), (7,4,4,3,3).
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MATHEMATICA
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(* first do *) Needs[DiscreteMath`Combinatorica`] (* then *) f[n_] := Length@ Select[ Partitions@n, (Length@ # > 1 && Last@# First@# == n) &]; Array[f, 72] - from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 15 2006
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CROSSREFS
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Cf. A000041, A116901, A116902.
Sequence in context: A081082 A049785 A036997 this_sequence A160210 A028928 A091379
Adjacent sequences: A116897 A116898 A116899 this_sequence A116901 A116902 A116903
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KEYWORD
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nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 14 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 15 2006
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