Divisor Count of 21,952

Example of Use of $\tau$ Function

 * $\tau \left({21 \, 952}\right) = 28$

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

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

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:
 * $21 \, 952 = 2^6 \times 7^3$

Thus:

The divisors of $21 \, 952$ can be enumerated as:
 * $1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 343, 392,$
 * $448, 686, 784, 1372, 1568, 2744, 3136, 5488, 10976, 21952$