Characteristic function of exact divisors

let d be an integer divisor of the integer n. We say that d is an exact divisor of n if gcd(d, n/d) = 1 i.e. if d and n/d are relatively prime. My question is related to the characteristic function of the exact divisors F(d,n) such that:

F(d,n) = 1 if d exact divisor of n, 0 else.
(d exact divisor also written as d||n)

Note that F(ab,nm) = F(a,n)F(b,m) if (n,m)=1, a ||n and b||m.

Is there a way to have an arithmetical expression of F(d,n) involving well known arithmetical functions.

Thanks for help.

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