How this calculation works
The calculation accumulates contributions by permitted part size. This prevents counting reorderings as new partitions.
THE FORMULA
Multiply the generating factors 1/(1−xᵏ) up to degree nA worked example
7 has 15 partitions. The expressions 3 + 4 and 4 + 3 count once.
Good to know
The empty partition of zero counts once.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count ways to write an integer as a sum of positive integers with order ignored.
The primary result is labeled “Partitions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The empty partition of zero counts once.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
7 has 15 partitions. The expressions 3 + 4 and 4 + 3 count once.
Which rule does this calculator apply?
Multiply the generating factors 1/(1−xᵏ) up to degree n