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 A140436 a(n) is the maximum number of partitions of n with the same product. 10
 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 12, 12, 15, 16, 19, 21, 25, 27, 30, 33, 36, 40, 45, 49, 58, 63, 72, 79, 91, 100, 114, 127, 147, 163, 183, 204, 229, 252, 281, 311, 343, 378, 418, 469, 517, 571, 633, 692, 763, 830, 918, 999, 1087, 1189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Giovanni Resta, Table of n, a(n) for n = 1..100 EXAMPLE There are two pairs of partitions of 6 that give the same product: the partitions {1,1,2,2} and {1,1,4} have product 4 and the partitions {2,2,2} and {2,4} have product 8. You can't find three different partitions of 6 that give the same product. Hence a(6) = 2. MATHEMATICA Table[Max[Transpose[Tally[Times @@@ IntegerPartitions[n]]][[2]]], {n, 60}] PROG (Haskell) import Data.List (sort, group) a140436 n = a140436_list !! (n-1) a140436_list = map (maximum . map length . group . sort . map product) \$                    tail pss where    pss = [] : map p [1..]    p u = [u] : [v : ps | v <- [1..u], ps <- pss !! (u - v), v <= head ps] -- Reinhard Zumkeller, Oct 10 2013 CROSSREFS Cf. A034891, A212721. Sequence in context: A116492 A103263 A173777 * A236916 A029083 A249040 Adjacent sequences:  A140433 A140434 A140435 * A140437 A140438 A140439 KEYWORD nice,nonn AUTHOR Tanya Khovanova, Jun 20 2008 STATUS approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)