Divisor Count of 40,315

Example of Use of $\tau$ Function

 * $\tau \left({40 \, 315}\right) = 8$

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:
 * $40 \, 315 = 5 \times 11 \times 733$

Thus:

The divisors of $40 \, 315$ can be enumerated as:
 * $1, 5, 11, 55, 733, 3665, 8063, 40 \, 315$