Divisor Count of 78

Example of Use of Divisor Counting Function

 * $\map \tau {78} = 8$

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:
 * $78 = 2 \times 3 \times 13$

Thus:

The divisors of $78$ can be enumerated as:
 * $1, 2, 3, 6, 13, 26, 39, 78$