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Some properties of the equation S(x)=k. (English)
Pi Mu Epsilon J. 11, No. 5, 265-270 (2001).
In 1979, Florentin Smarandache introduced a number theoretic function. For any positive integer n, the Smarandache function S(n) is defined as S(n)=k if k is the smallest positive integer such that n divides k!. Since then, some interesting properties have been discovered about this function. Just one example, for $x>4$, the expression $π$(x)=-1+$(Σ_{k=2}^x)\lbrackS(k)/k\rbrack$, where \lbrackx\rbrack is the greatest integer function, gives the exact number of primes less than or equal to x. In this note, we will look at some elementary properties associated with the equations S(x)=k. (From the introduction)
Classification: F60
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