Factorial: Difference between revisions
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==Behavior== | ==Behavior== | ||
===Initial values=== | ===Initial values=== | ||
The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]], <toggledisplay>3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000</toggledisplay> [[Oeis:A000142|View list on OEIS]]<section end="list"/> | |||
==Related notions== | ==Related notions== | ||
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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.