Banerjee, Debika; Minamide, Makoto On an analogue of Buchstab’s identity. (English) Zbl 1376.11069 Notes Number Theory Discrete Math. 22, No. 1, 8-17 (2016). Summary: In this paper, let \(p\) denote a prime. We shall consider sums of the type \(\Phi(x,y;f)=\sum_{n\geq x, p\mid n\Rightarrow p>y} f(n)\) and \(\psi(x,y;f)=\sum_{n\geq x, p\mid n\Rightarrow p<y} f(n)\) for certain kinds of arithmetical functions \(f\) and prove some identities for \(\Phi\) and \(\psi\) which are analogous to the ‘so-called’ Buchstab identity. As an application, we prove some formulas for square-free integers. MSC: 11N25 Distribution of integers with specified multiplicative constraints 11N37 Asymptotic results on arithmetic functions Keywords:Buchstab’s identity; square-free integers PDFBibTeX XMLCite \textit{D. Banerjee} and \textit{M. Minamide}, Notes Number Theory Discrete Math. 22, No. 1, 8--17 (2016; Zbl 1376.11069) Full Text: Link