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 A140437 a(n) is the maximal number of partitions of n of the same length with the same product. 1
 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; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS This sequence was inspired by John Conway's Wizards puzzle (see link). LINKS Tanya Khovanova, John Conway's Wizards Puzzle EXAMPLE The number 13 can be partitioned into 3 numbers with the same product in two ways: {1,6,6} and {2,2,9}. It can also 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. MATHEMATICA 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}] (* Robert G. Wilson v, Aug 19 2008 *) CROSSREFS Sequence in context: A087834 A172263 A337635 * A226763 A050500 A076885 Adjacent sequences:  A140434 A140435 A140436 * A140438 A140439 A140440 KEYWORD nonn AUTHOR Tanya Khovanova, Jun 20 2008, Jun 23 2008 EXTENSIONS More terms from Robert G. Wilson v, Aug 19 2008 STATUS approved

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Last modified January 16 14:30 EST 2022. Contains 350376 sequences. (Running on oeis4.)