THIRTY-NINE PERFECT NUMBERS AND THEIR DIVISORS

SYED ASADULLA

《International Journal of Mathematics and Mathematical Sciences》 1986卷 (1986/12) Pp. 205-206

https://doi.org/10.1155/S016117128600025X

摘要

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) =2p, whereτ(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.

關鍵字

Perfect number ； Marsenne prime ； Triangular number