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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 2,520.

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
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