Factorial: Difference between revisions
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* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group|exponent]] of the symmetric group of degree <math>n</math>. | * [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group|exponent]] of the symmetric group of degree <math>n</math>. | ||
* [[Maximum product over additive partitions]] | * [[Maximum product over additive partitions]] | ||
* [[ | * [[Landau's function]] is the maximum lcm over additive partitions. | ||
* [[Primorial]] is the product of the first few primes. | * [[Primorial]] is the product of the first few primes. | ||
Latest revision as of 17:58, 3 July 2012
Definition
Let be a nonnegative integer. The factorial of , denoted , and read as n factorial, is defined as the product of all the natural numbers from to . Note that is defined as .
is also the order of the symmetric group, or the group of all permutations, on a set of size .
Behavior
Initial values
The initial values of for are given as:
1, 2, 6, 24, 120, 720, 5040, 40320, 362880, [SHOW MORE]
Related notions
- lcm of all numbers so far: This is the exponential of the second Chebyshev function and also equals the exponent of the symmetric group of degree .
- Maximum product over additive partitions
- Landau's function is the maximum lcm over additive partitions.
- Primorial is the product of the first few primes.