carefree constant | strongly carefree constant

Define a carefree couple as a pair of positive integers (a, b) such that a and b are relatively prime (i.e., GCD(a, b) = 1) and a is squarefree. Similarly, define a strongly carefree couple as a pair (a, b) such that GCD(a, b) = 1 and both a and b are squarefree, and a weakly carefree couple as a pair (a, b) such that GCD(a, b) = 1 and at least of one a and b is squarefree. Let C_0(x) be the number of squarefree pairs, C_1(x) the number of carefree couples, C_2(x) the number of strongly carefree couples, and C_3(x) the number of weakly squarefree couples with a, b<=x, illustrated above.

prime products | squarefree