Divisor Count of 17,796,126,877,482,329,126,045

Example of Use of Divisor Counting Function

 * $\map \tau {17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 045} = 48$

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:
 * $17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 045 = 5 \times 17^2 \times 47 \times 53 \times 4 \, 944 \, 062 \, 119 \, 125 \, 691$

Thus: