Amount of ways N can be written as sum of two or more non-repeating integers

Question

For example, 5 can be written in 2 ways:

• 4 + 1
• 3 + 2

8 can be written in 5 ways:

• 7+1
• 6+2
• 5+3
• 5+2+1
• 4+3+1

How could this be determined for any positive integer N?

Answer 1

This is known as the number of strict partitions. Wikipedia contains a number of results on this. You can compute the number using dynamic programming.