|
|
|
Viewing Version
2
of
'$\tau$ function'
|
[ view '$\tau$ function'
|
back to history
]
| Title of object: |
$\tau$ function |
| Canonical Name: |
TauFunction |
| Type: |
Definition |
| Created on: |
2003-03-10 02:09:51.110695-05 |
| Modified on: |
2003-03-10 02:23:26.340681-05 |
| Classification: |
msc:11Z05 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
The $\tau$ function takes positive integers as its input and gives the number of positive divisors of its input as its output. For example, since 1, 2, and 4 are all of the positive divisors of 4, then $\tau (4)=3$.
The $\tau$ function behaves according to the following two rules:
1. If $p$ is a prime and $x$ is a nonnegative integer, then $\tau (p^x) = x+1$.
2. If $GCD(a,b)=1$, then $\tau(ab)=\tau(a)\tau(b)$. |
|
|
|
|
|
