partitions with the same product

[Max A.]

On 7/23/06, Joseph Biberstine <jrbibers at indiana.edu> wrote:

> If I'm understanding you and we trust my code, here are the results on 4
> to 100.  There are exactly three such partitions at these inputs: {39,
> 45, 49, 53, 62, 64, 65, 70, 71, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84,
> 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100},

I confirm this sequence.

> which is not in OEIS and gets no hits from Superseeker.
> No input under 100 has more than four such partitions;

Actually, no one of them have more than 3 such partitions. The
smallest number that has 4 partitions is 118.

It is worth to mention that for some numbers there are also several
different products. For example,

49=7+18+24   7*18*24=3024
49=8+14+27   8*14*27=3024
49=9+12+28   9*12*28=3024

49=9+20+20   9*20*20=3600
49=10+15+24 10*15*24=3600
49=12+12+25 12*12*25=3600

Max