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The weak factorial is a factorial-related function so-named by Cookie Fonster. It is equal to the least smallest number divisible by all numbers 1 through x. [1]

Formally:

$$wf(x) = LCM(x, wf(x-1))$$

$$wf(1) = 1$$

The first ten weak factorial numbers are 1, 2, 6, 12, 60, 60, 420, 840, 2520, and 2520.

It can be shown that value of this function increases only at arguments which are prime powers. Because of that, there will be long runs where the function is constant.

This function can be shown to be equal to $$e^{\psi(x)}$$, where $$\psi(x)$$ is the second Chebyshev function, so as a collorary from prime number theorem, it can be approximated by ex.

### SourcesEdit

1. Pointless Large Number Stuff by Cookiefonster, entry on 420
Main article: Factorial
Multifactorials: Double factorial · Multifactorial
Falling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial