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Search: id:A117086
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| A117086 |
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Number of partitions of n such that the largest part is a multiple of the smallest part. |
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+0
3
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| 1, 2, 3, 5, 6, 11, 12, 20, 26, 37, 45, 71, 84, 117, 152, 203, 253, 342, 421, 556, 694, 884, 1096, 1409, 1729, 2168, 2672, 3327, 4061, 5039, 6114, 7514, 9110, 11098, 13400, 16275, 19537, 23575, 28245, 33929, 40465, 48424, 57552, 68569, 81296, 96449
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also number of partitions of n such that the number of parts is a multiple of the multiplicity of the largest part. Example: a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [3,3,1], [2,2,2,1], and [2,2,1,1,1] do not qualify (3,4,5 are not multiples of 2,3,2, respectively). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 2006
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FORMULA
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G.f.: Sum(Sum(x^((l+1)*k)/Product(1-x^i,i=k..l*k),k=1..infinity),l=0..infinity).
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EXAMPLE
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a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [5,2],[4,3], and [3,2,2] do not qualify.
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MAPLE
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f:=add(add(x^((l+1)*k)/mul(1-x^i, i=k..l*k), k=1..51), l=0..51):s:=series(f, x, 51):for m from 1 to 50 do c:=coeff(s, x, m):printf(`%d, `, c); od: (Jovovic) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 2006
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CROSSREFS
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Cf. A118096.
Cf. A000041.
Sequence in context: A033159 A083710 A127524 this_sequence A081026 A137808 A091909
Adjacent sequences: A117083 A117084 A117085 this_sequence A117087 A117088 A117089
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 17 2006
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 2006
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