\(2\) and \(9\) are the only biunitary superperfect
numbers

Abstract. We shall show that \(2\) and \(9\) are the only biunitary superperfect numbers and give biunitary multiply superperfect numbers below \(2^{32}\), posing some related problems.

Key words and phrases. Odd perfect numbers, biunitary superperfect numbers, unitary divisors, biunitary divisors, the sum of divisors, iterations of arithmetic functions.