Problem 374

[agebhar1]

In the problem description of Problem 374 (View Problem) the following statements are given

Partitions that differ only in the order of their summands are considered the same. A partition of n into distinct parts is a partition of n in which every part occurs at most once.

and

For n=10 the partition with the largest product is 10=2+3+5, which gives f(10)=30 and m(10)=3.
And their product, f(10)·m(10) = 30·3 = 90

Whats wrong with this alternative partition of 10?

10 = 2+2+3+3 -> f(10) = 36, m(10) = 4

Another question is, since

m

should be a function what is the result of partition e.g. 4?

4 = 4 -> f(4) = 4, m(4) = 1
4 = 2+2 -> f(4) = 4, m(4) = 2

Thanks,
Andreas

[jaap]

Whats wrong with this alternative partition of 10?
10 = 2+2+3+3 -> f(10) = 36, m(10) = 4

This:

Let f(n) be the maximum product of the parts of any such partition of n into distinct parts

Another question is, since m should be a function what is the result of partition e.g. 4?
4 = 4 -> f(4) = 4, m(4) = 1
4 = 2+2 -> f(4) = 4, m(4) = 2

I don't think m will be ambiguous if you have distinct parts in the maximum product.

[agebhar1]

Let f(n) be the maximum product of the parts of any such partition of n into distinct parts

I missunderstood distinct. I thought it refers to the order of summands of the partition.

Thanks for the clarification.
Andreas