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2009-05-20, 06:47   #20
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2·1,061 Posts

Quote:
 Originally Posted by 10metreh What is the word Guy and Selfridge suggest using for things like 2^2*3, which would be classified as having the "guide" 2^2 (seems completely mad)?
Here's the definition from the article:
Quote:
 Originally Posted by Guy&Selfridge Define a guide to be $2^a$, together with a subset of the prime factors of $\ \sigma(2^a)$. A driver is defined as a number $\ 2^av$ with $\ a>0$, $v$ odd, $v|\sigma(2^a)$ and $2^{a-1}|\sigma(v)$. The last requirement is included so that the power of the prime 2 will tend to persist at least as well as it does for the driver 2 itself, for which the condition is trivially satisfied.
Further down, they give these as guides:
Code:
$2^2$

$2^3$

$2^35$

$2^4$

$2^53$

$2^57$
So, I have been a little, um, imprecise, in calling, for example, $2^23$, a guide. The guide is actually $2^2$...

And I actually have been lax: the drivers include the even perfect numbers.....