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Primitive Abundant Numbers

An integer's PD's (Proper Divisors) are all those integers less than itself which divided into it exactly.

An Abundant Number is one which is less than the sum of its PD's.

A Deficient Number is one which is greater than the sum of its PD's.

A Primitive Abundant Number is an Abundant Number whose PD's are all Deficient Numbers.

Example: 20 is Abundant because the sum of its PD's is 1+2+4+5+10 = 22.  All the PD's are themselves Deficient Numbers. Thus, 20 is a Primitive Abundant Number.

What is the smallest interval between two successive Primitive Abundant Numbers less than 10,000?





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Last Updated: December 19th, 2010.