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

%I A140436 #6 May 12 2016 13:35:23
%S A140436 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,
%T A140436 45,49,58,63,72,79,91,100,114,127,147,163,183,204,229,252,281,311,343,
%U A140436 378,418,469,517,571,633,692,763,830,918,999,1087,1189
%N A140436 a(n) is the maximum number of partitions of n with the same product.
%H A140436 Giovanni Resta, <a href="/A140436/b140436.txt">Table of n, a(n) for n = 1..100</a>
%e A140436 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.
%t A140436 Table[Max[Transpose[Tally[Times @@@ IntegerPartitions[n]]][[2]]], {n, 60}]
%o A140436 (Haskell)
%o A140436 import Data.List (sort, group)
%o A140436 a140436 n = a140436_list !! (n-1)
%o A140436 a140436_list = map (maximum . map length . group . sort . map product) $
%o A140436                    tail pss where
%o A140436    pss = [] : map p [1..]
%o A140436    p u = [u] : [v : ps | v <- [1..u], ps <- pss !! (u - v), v <= head ps]
%o A140436 -- _Reinhard Zumkeller_, Oct 10 2013
%Y A140436 Cf. A034891, A212721.
%K A140436 nice,nonn
%O A140436 1,4
%A A140436 _Tanya Khovanova_, Jun 20 2008