In his Introduction to Arithmetic, Nicomachus wrote the following:

Nicomachus is clearly implying that the nth perfect number has n digits. We already know this is wrong; we discovered in Chapter 2 that the fifth perfect number is 33550336. According to Dickson, 1999, Iamblichus in his Commentary on Nicomachus states this even more explicitly, and the mistake was subsequently repeated by Boethius in the fifth century. In the twelfth century, Abraham ben Meir ibn Ezra made the same claim in his commentary to the Pentateuch. In the fourteenth century, Thomas Bradwardine, mathematician and physicist, repeated the claim in his book Arithmetica Speculativa. Bradwardine became Archbishop of Canterbury but died shortly after of the Black Death in 1349.

Despite being wrong, this claim by Nicomachus is important because it is the very first of its kind. It examines the distribution of perfect numbers among all the integers. Because of Euler's theorem (see Chapter 2), we know that even perfect numbers correspond to prime Mersenne numbers.