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, 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

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