Converegence of a series leading to an analogue of Ramanujan's assertion on squarefree integers

Abstract

Let d be a squarefree integer. We prove thatconverges to zero, where n ′ is the product of prime divisors of n with (The convergence (i) leads to a proof that asymptotically half the squarefree ideals have an even number of prime ideal factors (analogue of Ramanujan's assertion).