Divisor Count of 21,952

Example of Use of Divisor Counting Function

 * $\map {\sigma_0} {21 \, 952} = 28$

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

Thus:

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