A140436 a(n) is the maximum number of partitions of n with the same product.

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

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