Divisor Count of 21,952

Example of Use of Divisor Count Function

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

where $\sigma_0$ denotes the divisor Count function.

$\ds \map {\sigma_0} n = \prod_{j \mathop = 1}^r \paren {k_j + 1}$

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:

$\ds \map {\sigma_0} {21 \, 952}$

$=$

$\ds \map {\sigma_0} {2^6 \times 7^3}$

$\ds $

$=$

$\ds \paren {6 + 1} \paren {3 + 1}$

$\ds $

$=$

$\ds 28$

The divisors of $21 \, 952$ can be enumerated as:

$1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 343, 392,$

$448, 686, 784, 1372, 1568, 2744, 3136, 5488, 10976, 21952$

$\blacksquare$