Divisor Count of 997,920

Example of Use of $\tau$ Function

 * $\tau \left({997 \, 920}\right) = 240$

where $\tau$ denotes the $\tau$ Function.

Proof
From Tau Function from Prime Decomposition:
 * $\displaystyle \tau \left({n}\right) = \prod_{j \mathop = 1}^r \left({k_j + 1}\right)$

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:
 * $997 \, 920 = 2^5 \times 3^4 \times 5 \times 7 \times 11$

Thus: