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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
OFFSET
1,4
LINKS
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
Sequence in context: A116492 A103263 A173777 * A236916 A029083 A249040
KEYWORD
nice,nonn
AUTHOR
Tanya Khovanova, Jun 20 2008
STATUS
approved