Sunday, March 18, 2012

Multiply perfect numbers

The first three multiply perfect numbers are 1, 6, and 120. These three numbers are both factorials and triangular. They also appear to be the only numbers that exhibit that property.

The numbers 1 and 6 are the only numbers that are triangular and factorial with respect to the same argument because 1 is both the sum and the product of the first one numbers and 6 is both the sum and product of the first three numbers.

The only number that appears to be factorial and triangular to a different argument is 120 which is the product of the first five numbers and the sum of the first fifteen. Interestingly, 120 is also a tetrahedral number.

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