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:


  • Combinatorics
  • Integers
  • Integer Sequences

  • Perfect Numbers on Wolfram MathWorld
  • Pascal's Triangle on Wolfram MathWorld
  • Figurate Numbers on Wolfram MathWorld
  • 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.

    Generate Pascal's triangle:

    Compute Pascal's triangle modulo an integer: