Examples for

# Special Numbers

Many numbers are generated from or represented by symbolic, geometric or otherwise interesting patterns and criteria. These live under the umbrella term "special numbers." Wolfram|Alpha is prepared for queries about different kinds of such numbers, such as polygonal numbers, perfect numbers, Lucas numbers, numbers from Pascal's triangle and more.

### Figurate Numbers

Query polygonal numbers and do calculations with them or check whether values are members of a figurate number class.

#### Compute a polygonal number:

#### Determine whether a number belongs to a given class:

### Sets of Integers

Find a number or a set of numbers meeting certain criteria or check whether an individual value meets specified criteria.

#### Find a number matching specified criteria:

#### Find numbers matching specified criteria:

### Perfect Numbers

Analyze numbers in terms of their relationship with the sum of their divisors.

#### Determine whether a number belongs to a given class:

### Sums & Products of Number Sets

Perform operations on defined sets of numbers.

#### Take the sum or product of a sequence of numbers of a given type:

### RELATED EXAMPLES

### RELATED WOLFRAM RESOURCES

### Pascal's Triangle

Query elements and rows of this famous triangle or analyze the values of its elements subject to a modulus or other condition.