Divisor Count of 720,720

Example of Use of Divisor Counting Function

 * $\map \tau {720 \, 720} = 240$

where $\tau$ denotes the divisor counting (tau) function.

Proof
From Divisor Counting Function from Prime Decomposition:
 * $\ds \map \tau n = \prod_{j \mathop = 1}^r \paren {k_j + 1}$

where:
 * $r$ denotes the number of distinct prime factors in the prime decomposition of $n$
 * $k_j$ denotes the multiplicity of the $j$th prime in the prime decomposition of $n$.

We have that:
 * $720 \, 720 = 2^4 \times 3^2 \times 5 \times 7 \times 11 \times 13$

Thus: