On the Sandor-Smarandache Function

Abstract

In the current literature, a new Smarandache-type arithmetic function, involving binomial coefficients, has been proposed by Sandor. The new function, denoted by SS(n), is named the Sandor-Smarandache function. It has been found that, like many Smarandache-type functions, SS(n) is not multiplicative. Sandor found SS(n) when n (≥3) is an odd integer. Since then, the determination of SS(n) for even n remains a challenging problem. It has been shown that the function has a simple form even when n is even and not divisible by 3. This paper finds SS(n) in some particular cases of n, and finds an upper bound of SS(n) for some special forms of n. Some equations involving the Sandor-Smarandache function and pseudo-Smarandache function have been studied. A list of values of SS(n) for n = 1(1)480, calculated on a computer, is appended at the end of the paper.