OFFSET
1,12
COMMENTS
This sequence was inspired by John Conway's Wizards puzzle (see link).
LINKS
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
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Jun 20 2008, Jun 23 2008
EXTENSIONS
More terms from Robert G. Wilson v, Aug 19 2008
STATUS
approved