Unitarism and Infinitarism

as N → ∞, where γ is the Euler-Mascheroni constant. Let us introduce a more refined notion of divisibility. A divisor k of n is unitary if k and n/k are coprime, that is, if gcd(k, n/k) = 1. This condition is often written as k||n. The number d∗(n) of unitary divisors of n is 2, where ω(n) is the number of distinct prime factors of n. This fact is easily seen to be true: If p1 1 p a2 2 · · · pr r is the prime factorization of n, then the unitary divisors of n are of the form p11 1 p ε2a2 2 · · · prr r , where each εs is either 0 or 1. There are 2 possible choices for the r-tuple (ε1, ε2, . . . , εr); hence the result follows. We have [1, 2, 3, 4, 5]