Divisor Count of 714

Example of Use of Divisor Counting Function

 * $\map \tau {714} = 16$

where $\tau$ denotes the divisor counting function.

Proof
From Tau 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:
 * $714 = 2 \times 3 \times 7 \times 17$

Thus:

The divisors of $714$ can be enumerated as:
 * $1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714$