Divisor Count of 570

Example of Use of $\tau$ Function

 * $\map \tau {570} = 16$

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

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

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:
 * $570 = 2 \times 3 \times 5 \times 19$

Thus:

The divisors of $570$ can be enumerated as:
 * $1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570$