Divisor Count of 17,796,126,877,482,329,126,049

Example of Use of Divisor Counting Function

 * $\map {\sigma_0} {17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 049} = 48$

where $\sigma_0$ denotes the divisor counting function.

Proof
From Divisor Counting Function from Prime Decomposition:
 * $\ds \map {\sigma_0} n = \prod_{j \mathop = 1}^r \paren {k_j + 1}$

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:
 * $17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 049 = 3 \times 13^2 \times 241 \times 557 \times 261 \, 484 \, 106 \, 225 \, 711$

Thus: