View Single Post
Old 2009-05-20, 06:47   #20
schickel
 
schickel's Avatar
 
"Frank <^>"
Dec 2004
CDP Janesville

2·1,061 Posts
Default

Quote:
Originally Posted by 10metreh View Post
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.....
schickel is offline   Reply With Quote