

A140437


a(n) is the maximal number of partitions of n of the same length with the same product.


1



1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 14, 16, 18, 19, 21, 24, 26, 28, 30, 31, 36, 38, 41, 44, 49, 51, 54, 60, 65, 70, 76, 81, 89, 93, 102, 111, 120, 131, 144, 155, 167, 182, 201, 216, 236, 254, 279, 303, 336, 363, 402, 431, 476
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OFFSET

1,12


COMMENTS

This sequence was inspired by John Conway's Wizards puzzle (see link).


LINKS

Table of n, a(n) for n=1..79.
Tanya Khovanova, John Conway's Wizards Puzzle


EXAMPLE

The number 13 can be partitioned into 3 numbers with the same product in two ways: {1,6,6} and {2,2,9}. It can also be partitioned into 5 numbers with the same product in two ways: {1,1,3,4,4} and {1,2,2,2,6}. 13 can't have 3 different partitions of the same length with the same product. Hence a(13) = 2.


MATHEMATICA

Table[Max[ Transpose[ Flatten[Table[ Tally[Apply[Times, IntegerPartitions[k, {n}], 2]], {n, k}], 1]][[2]]], {k, 60}]
Table[ Max[ Transpose[ Flatten[ Table[ Tally[ Apply[ Times, IntegerPartitions[k, {n}], 2]], {n, k}], 1]][[2]]], {k, 60}] (* Robert G. Wilson v, Aug 19 2008 *)


CROSSREFS

Sequence in context: A087834 A172263 A337635 * A226763 A050500 A076885
Adjacent sequences: A140434 A140435 A140436 * A140438 A140439 A140440


KEYWORD

nonn


AUTHOR

Tanya Khovanova, Jun 20 2008, Jun 23 2008


EXTENSIONS

More terms from Robert G. Wilson v, Aug 19 2008


STATUS

approved



