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p. 273. Perfect and not so perfect numberslocked

  • Peter M. Higgins

Abstract

‘Perfect and not so perfect numbers’ examines the concept of perfect numbers. Perfect numbers are numbers which are the sum of their proper factors. Euclid showed that perfect numbers had a relationship with a special type of prime called a Mersenne number. Euler expanded on this to give a direct relationship between Mersenne numbers and perfect numbers. Amicable pairs are pairs of numbers whose proper factors sum to each other. A number's aliquot sequence can be found by repeatedly summing a number's factors to get a new number. Numbers can be deficient, perfect, or abundant, depending on the sum of their factors.

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