Define the following funtion f(n) = the finite product of sin(pi*C/n) from n = 2 to n, where C is any integer >= 2. As it turns out, for each integer C, the product terminates to zero at n the smallest prime factor of C. For example, suppose you consider C = 3 f(2) = sin(pi*3/2) = 1 f(3) = sin(pi*3/2)*sin(pi*3/3) = 0 f(4) = sin(pi*3/2)*sin(pi*3/3)*sin(pi*3/4) = 0 . . . f(n) = 0 for any integer greater than 2 If you define F as the family of functions of the form above for all positive integers C >= 2, then the set of all those functions will have positive values for integers n in the closed interval [2, "smallest prime factor of C"), and will be zero for all other integers "greater than the smallest prime factor of C." The question I have is as follows: n! (n factorial) is defined for all integer n greater than or equal to 0. However, the gamma function is considered the generalized factorial function, because it reduces to n factorial for positive integers. I was wondering if it is possible to construct a gamma-like function for f(n), that is, a “generalized function for f(n)” with C being a free parameter? Inquisitively, Edwin p.s. would such a function have any connection to the Riemann Zeta Function?