Editing Multiply perfect number (section)

===Unitary multiply perfect numbers===
A similar extension can be made for [[unitary perfect number]]s. A positive integer ''n'' is called a '''unitary multi''' {{nowrap|''k''-'''perfect'''}} '''number''' if σ<sup>*</sup>(''n'') = ''kn'' where σ<sup>*</sup>(''n'') is the sum of its [[unitary divisor]]s. (A divisor ''d'' of a number ''n'' is a unitary divisor if ''d'' and ''n/d'' [[coprime integers|share no common factors]].). 

A '''unitary multiply perfect number''' is simply a unitary multi {{nowrap|''k''-perfect}} number for some positive integer ''k''. Equivalently, unitary multiply perfect numbers are those ''n'' for which ''n'' divides σ<sup>*</sup>(''n''). A unitary multi {{nowrap|2-perfect}} number is naturally called a '''unitary perfect number'''. In the case ''k'' > 2, no example of a unitary multi {{nowrap|''k''-perfect}} number is yet known. It is known that if such a number exists, it must be [[parity (mathematics)|even]] and greater than 10<sup>102</sup> and must have more than forty four odd prime factors. This problem is probably very difficult to settle. The concept of unitary divisor was originally due to [[Ramaswamy S. Vaidyanathaswamy|R. Vaidyanathaswamy]] (1931) who called such a divisor as block factor. The present terminology is due to E. Cohen (1960).

The first few unitary multiply perfect numbers are:
:1, 6, 60, 90, 87360 {{OEIS|A327158}}