Infinite Series and Arithmetical Functions

Let n be any positive integer. Then n can be written in one, and only one way

n = P_n1 V1_Pn2V₂........P_nk V_k           (1.1)

where P_n1, P_n2,.........P_nk are distinct primes.

Throughout this paper the following notations are used :-

[x]=the integer equal to or immediately smaller than the real number x.