How this calculation works
Count unordered sums using each positive part at most once.
THE FORMULA
Multiply factors (1+xᵏ) through k=n and read the coefficient of xⁿA worked example
Six has four such sums: 6, 5+1, 4+2 and 3+2+1.
Good to know
Zero has one empty partition.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count unordered sums using each positive part at most once.
The primary result is labeled “Partitions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Zero has one empty partition.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Six has four such sums: 6, 5+1, 4+2 and 3+2+1.
Which rule does this calculator apply?
Multiply factors (1+xᵏ) through k=n and read the coefficient of xⁿ