Some Results on the Unitary Analogue of the Lehmer Totient Problem

A composite positive integer n with more than one prime divisor is called Subbarao if ϕ∗(n) divides n−1, where ϕ∗(n) is the unitary analogue of the Euler’s totient function. No Subbarao number is known, nor has it been proved that they don’t exist. We find some possible forms of Subbarao numbers. We also show that there is no Subbarao number in the balancing sequence (Bn)n≥0 given by B0=0, B1=1 and the recursive relation Bn=6Bn−1−Bn−2 for n≥2.