Yamada, Tomohiro 2 and 9 are the only biunitary superperfect numbers. (English) Zbl 1413.11011 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 48, 247-256 (2018). A positive divisor \(d\) of a positive integer \(N\) is called a unitary divisor if the greatest common divisor of \(d\) and \(N/d\) equals \(1\), and a positive divisor \(d\) of \(N\) is called a biunitary divisor if the greatest common unitary divisor of \(d\) and \(N/d\) equals \(1\). Let \(\sigma^{\ast\ast}(N)\) denote the sum of the biunitary divisors of \(N\). A positive integer \(N\) is said to be biunitary perfect if \(\sigma^{\ast\ast}(N)=2N\). C. R. Wall [Proc. Am. Math. Soc. 33, 39–42 (1972; Zbl 0214.06404)] proved (applying elementary methods) that \(6\), \(60\) and \(90\) are the only biunitary perfect numbers. A positive integer \(N\) is said to be biunitary superperfect if \(\sigma^{\ast\ast}(\sigma^{\ast\ast}(N))=2N\). The present author shows (applying also only elementary methods) that \(2\) and \(9\) are the only biunitary superperfect numbers. Reviewer: Pentti Haukkanen (Tampere) MSC: 11A25 Arithmetic functions; related numbers; inversion formulas Keywords:unitary divisors; biunitary divisors; sum of divisors type functions; iterates of arithmetic functions; biunitary superperfect numbers Citations:Zbl 0214.06404 PDFBibTeX XMLCite \textit{T. Yamada}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 48, 247--256 (2018; Zbl 1413.11011) Full Text: arXiv Online Encyclopedia of Integer Sequences: Bi-unitary sigma: sum of the bi-unitary divisors of n. Numbers m such that A188999(A188999(m)) = k*m for some k where A188999 is the bi-unitary sigma function. a(n) is the least k such that A188999(A188999(k)) = n*k, where A188999 is the bi-unitary sigma function, or 0 if no such k exists.