Some Pythagorean type equations concerning arithmetic functions

We investigate some equations involving the number of divisors d(n); sum σ(n); Euler's totient function ϕ(n); distinct prime factors ω(n); and all (counted with multiplicity) Ω(n). The first part deals equation f(xy) + f(xz) = f(yz). In second part, as an analogy to x2 y2 z2, we study f(x2) f(y2) f(z2) its generalization higher degrees more terms. use just elementary methods basic facts about above functions indicate why how discuss this topic in group sessions or special maths classes secondary schools framework inquiry based learning.
 Subject Classification: 97F60, 11A25