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Search: id:A140437
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| A140437 |
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a(n) is the maximal number of partitions of n of the same length with the same product. |
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1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 14, 16, 18, 19, 21, 24, 26, 28, 30, 31, 36, 38, 41, 44, 49, 51, 54, 60, 65, 70, 76, 81, 89, 93, 102, 111, 120, 131, 144, 155, 167, 182, 201, 216, 236, 254, 279, 303, 336, 363, 402, 431, 476
(list; graph; listen)
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OFFSET
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1,12
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COMMENT
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This sequence was inspired by John Conway's Wizards puzzle (see link).
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LINKS
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Tanya Khovanova, John Conway's Wizards Puzzle
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EXAMPLE
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Number 13 can be partitioned into 3 numbers with the same product in two ways: {1,6,6} and {2,2,9}. It also can be partitioned into 5 numbers with the same product in two ways: {1,1,3,4,4} and {1,2,2,2,6}. 13 can't have 3 different partitions of the same length with the same product. Hence a(13) = 2.
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MATHEMATICA
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Table[Max[ Transpose[ Flatten[Table[ Tally[Apply[Times, IntegerPartitions[k, {n}], 2]], {n, k}], 1]][[2]]], {k, 60}]
Table[ Max[ Transpose[ Flatten[ Table[ Tally[ Apply[ Times, IntegerPartitions[k, {n}], 2]], {n, k}], 1]][[2]]], {k, 60}] - from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 19 2008
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CROSSREFS
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Sequence in context: A117707 A163352 A087834 this_sequence A050500 A076885 A051889
Adjacent sequences: A140434 A140435 A140436 this_sequence A140438 A140439 A140440
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KEYWORD
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nonn
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 20 2008, Jun 23 2008
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EXTENSIONS
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More terms from from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 19 2008
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