Here’re some maths definitions that I want to jot down before I have to return the marvellous *The Man Who Loved Only Numbers*, Paul Hoffman (Hyperion, 1998) to the similarly marvellous Leeds Library.

Pythagoras saw perfection in any integer that equaled the sum of all the *other* integers that divided evenly into it. The first perfect number is 6… The second perfect number is 28.

Then there’s:

Smith numbers… began with a phone number. In 1982, Albert Wilansky… noticed that the phone number of his brother-in-law had the peculiar property that the sum of its digits was equal to the sum of the digits of its prime factors. Got that?

Yep, think so, thanks. Then there’s *friendly numbers*:

These numbers have a special mathematical property: each is equal to the sum of the other’s proper divisors (divisors other than the number itself).

The two smallest pairs of friendly numbers are 220 and 284, and 1,184 and 1,210.

“There comes a time when for every addition of knowledge you forget something that you knew before,” said Sherlock Holmes (echoing the sage point made here). “It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones. A man should keep his little brain attic stocked with all the furniture that he is likely to use, and the rest he can put away in the lumber room of his library, where he can get at it if he wants it.”

Or, in this case, the lumber room of his Clutterbuck.

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