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e-Perfect Number

A number is called an -perfect number if , where is the sum of the e-Divisors of . If is squarefree, then . As a result, if is -perfect and is squarefree with , then is -perfect.

The first few -perfect numbers are 36, 180, 252, 396, 468, ... (Sloane's A054979). There are no odd -perfect numbers. The first few primitive -perfect numbers are 36, 1800, 2700, 17424, ... (Sloane's A054980).

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