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.
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