Lets take a number 12 as an example .
It can be partitoned into three integer summands in 12 ways:
Multiplying the 3 members of each partitions results in 12 distinct numbers: 10,18,...60,64.
On the other hand the same treatment applied to number 13 produces a pair of equal results: 13=1+6+6=2+2+9 and 1*6*6=2*2*9=36 (a well known problem of children's ages).
Find the smallest number which has 3 distinct partitions into 3 parts, each of them with the same product.
Bonus: list all numbers below 1000 boasting this feature.
(In reply to re: Answer to the bonus.
by Ady TZIDON)
I've now verified that all the numbers up through 2000 that fail to boast the feature are 102 or less.
I've tried to make the comment on OEIS, but I've forgotten my password, and the temporary password they sent doesn't work. I'll try it again tomorrow.
BTW, the sequence for those that do meet the criterion is A119028
Edited on November 22, 2018, 6:44 pm
Posted by Charlie
on 2018-11-22 18:42:00