Editing Multiply perfect number (section)

===Triperfect numbers===
A number ''n'' with σ(''n'') = 3''n'' is '''triperfect'''. There are only six known triperfect numbers and these are believed to comprise all such numbers:

: 120, 672, 523776, 459818240, 1476304896, 51001180160 {{OEIS|A005820}}

If there exists an odd perfect number ''m'' (a famous [[open problem]]) then 2''m'' would be {{nowrap|3-perfect}}, since σ(2''m'') = σ(2)σ(''m'') = 3×2''m''. An odd triperfect number must be a [[square number]] exceeding 10<sup>70</sup> and have at least 12 distinct prime factors, the largest exceeding 10<sup>5</sup>.<ref>{{harvnb|Sándor|Mitrinović|Crstici|2006|pp=108–109}}</ref>