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Revision difference : $\tau$ function |
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Version 1 |
| 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 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: |
The $\tau$ function behaves according to the following two rules: |
| 1. If $p$ is a prime and $x$ is a nonnegative integer, then $\tau (p^x) = x+1$. |
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 $\tau(ab)=\tau(a)\tau(b)$. |
2. If $GCD(a,b)=1$, then $\tau(ab)=\tau(a)\tau(b)$. |
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