ABSTRACT
Ever since Greek times the so-called perfect numbers have been objects of numerological speculation. In 2000 years no great use has ever been found for them, but they continue to mystify and fascinate people who are interested in the ‘personality’ of integers. The perfect numbers have considerable mystique since they are rarer by far than any classes of deficient or abundant numbers. Whether there is a critical ratio, equal to the sum of all the divisors divided by the number, which weird numbers cannot occur is not known. Another peculiar property of weirds is that all the known weirds are even. Although the weird numbers are a very small fraction of all the abundant numbers in any range of interest, it is nevertheless possible to establish that they do exist to arbitrarily high values.
