## A Conversation for Perfect Numbers

### Perhaps I missed it?

FordsTowel Started conversation Feb 19, 2004

Hi there,

Lovely piece, on a complex subject.

Somehow I must have missed you covering this; but if the definition of a perfect number is: 'If the sum of the divisors exactly equals the number, the number is called perfect', wouldn't One qualify as an odd perfect number?

Just wondering what I missed.

### Perhaps I missed it?

mathsmoose Posted Feb 26, 2004

You may have noticed that for the perfect number 6 the factors added together were 1, 2 and 3. Six is not counted in the list.

In other words the number you are checking isn't it self counted and thus for 1, 1 cannot be counted and the answer is 0 (a deficient number).

### Perhaps I missed it?

Gnomon - time to move on Posted Mar 22, 2004

It does actually say it in the entry:

"Every number divides evenly into itself, but N is not normally included in the list of divisors of N."

### Perhaps I missed it?

CRGreathouse Posted Nov 10, 2005

A number is perfect if it is the sum of its proper divisors n=s(n), or half the sum of its divisors 2n=sigma(n).

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