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

Author

Tanya Khovanova, Jun 20 2008

Keywords

• nice
• nonn

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A034891, A212721.

Programs

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

Mathematica

Table[Max[Transpose[Tally[Times @@@ IntegerPartitions[n]]][[2]]], {n, 60}]