The Smarandache function μ(n) is the function first considered by Lucas, Neuberg, and Kempner and subsequently rediscovered by Smarandache that gives the smallest value for a given n at which n|μ(n)! (i.e., n divides μ(n) factorial). For example, the number 8 does not divide 1!, 2!, 3!, but does divide 4! = 4·3·2·1 = 8·3, so μ(8) = 4.

factorial | greatest prime factor | pseudosmarandache function | Smarandache ceil function | Smarandache constants | Smarandache-Kurepa function | Smarandache near-to-primorial function | Smarandache-Wagstaff function