chapter  9
15 Pages

Numbers Perfect, Friendly, and Weird

WithMalcolm E Lines

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. Every integer seems to have a distinct character, but the label of perfection is not to be bestowed without due consideration, and the origin possibly goes back to biblical times and the statement that God created the world in six days. Six, you see, is the first (that is smallest) perfect number, and this perfection surrounds the fact that six is equal to the sum of its divisors, which are all those integers which divide it exactly (namely 1, 2, and 3). What is more, for this case alone the product of these divisors (that is to say 1×2×3) is also equal to the same number 6 and, as Isaac Asimov has said, ‘God could hardly be expected to resist all that’.