Divisor Count of 40,313

Example of Use of Divisor Counting Function

 * $\map \tau {40 \, 313} = 8$

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:
 * $40 \, 313 = 7 \times 13 \times 443$

Thus:

The divisors of $40 \, 313$ can be enumerated as:
 * $1, 7, 13, 91, 443, 3101, 5759, 40 \, 313$