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Thirty-nine perfect numbers and their divisors

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  • Syed Asadulla

Abstract

The following results concerning even perfect numbers and their divisors are proved: (1) A positive integer n of the form 2 p − 1 ( 2 p − 1 ) , where 2 p − 1 is prime, is a perfect number; (2) every even perfect number is a triangular number; (3) τ ( n ) = 2 p , where τ ( n ) is the number of positive divisors of n ; (4) the product of the positive divisors of n is n p ; and (5) the sum of the reciprocals of the positive divisors of n is 2 . Values of p for which 30 even perfect numbers have been found so far are also given.

Suggested Citation

  • Syed Asadulla, 1986. "Thirty-nine perfect numbers and their divisors," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-2, January.
    • Handle: RePEc:hin:jijmms:876283
    DOI: 10.1155/S016117128600025X
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