Let n ≥ 1 be an integer. Define Ï•2(n) to be the number of positive integers x, 1 ≤ x ≤ n, for which both 6x−1 and 6x+1 are relatively prime to 6n. The primary goal of this study is to show that Ï•2 is a multiplicative function, that is, if gcd(m, n) = 1, then Ï•2(mn) = Ï•2(m)Ï•2(n).
Key words: Euler phi-function, multiplicative function.
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