Editing Multiply perfect number (section)

{{Short description|Number whose divisors add to a multiple of that number}}
[[File:Multiply perfect number Cuisenaire rods 6.png|thumb|Demonstration, with [[Cuisenaire rods]], of the {{nowrap|2-perfection}} of the number 6]]

In [[mathematics]], a '''multiply perfect number''' (also called '''multiperfect number''' or '''pluperfect number''') is a generalization of a [[perfect number]].

For a given [[natural number]] ''k'', a number ''n'' is called {{nowrap|''k''-perfect}} (or {{nowrap|''k''-fold}} perfect) if the sum of all positive [[divisor]]s of ''n'' (the [[divisor function]], ''σ''(''n'')) is equal to ''kn''; a number is thus [[perfect number|perfect]] [[if and only if]] it is {{nowrap|2-perfect}}. A number that is {{nowrap|''k''-perfect}} for a certain ''k'' is called a multiply perfect number. As of 2014, {{nowrap|''k''-perfect}} numbers are known for each value of ''k'' up to 11.<ref name=fl/>

It is unknown whether there are any [[parity (mathematics)|odd]] multiply perfect numbers other than 1. The first few multiply perfect numbers are:
:1, 6, 28, 120, 496, 672, 8128, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240, ... {{OEIS|A007691}}.