eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-06-02 3 2 68 69 10.12691/tjant-3-2-6 TJANT2015326 article Azizul Hoque ahoque.ms@gmail.com, himashree.kalita28@gmail.com 1 Himashree Kalita ahoque.ms@gmail.com, himashree.kalita28@gmail.com 1 Department of Mathematics, Gauhati University, Guwahati, India In this paper we introduce two new Arithmetic functions, that is, Quasi-Multiplicative (QM) and omega functions. The Omega function is based on Euler's Phi function and is used to find the sum of coprime integers. Euler's Phi function, Dedekind's psi function, the sigma function and -function play significant role in this work. http://pubs.sciepub.com/tjant/3/2/6/tjant-3-2-6.pdf arithmetic function quasi-multiplicative function omega function