  Let [t] be the integral part of the real number t and let 1 P be the
characteristic function of the primes. Denote by $\pi$ G (x) the number of
primes in the floor function set G(x) := {[ x n ] : 1 n x} and by S 1 P (x) the
number of primes in the sequence {[ x n ]} n 1. Very recently, Heyman proves
