Divisor Count of 244

Example of Use of Divisor Count Function

$\map {\sigma_0} {244} = 6$

where $\sigma_0$ denotes the divisor count function.

Proof

From Divisor Count 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:

$244 = 2^2 \times 61$

Thus:

\(\ds \map {\sigma_0} {244}\)

\(=\)

\(\ds \map {\sigma_0} {2^2 \times 61^1}\)

\(\ds \)

\(=\)

\(\ds \paren {2 + 1} \paren {1 + 1}\)

\(\ds \)

\(=\)

\(\ds 6\)

The divisors of $244$ can be enumerated as:

$1, 2, 4, 61, 122, 244$

This sequence is A018352 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

$\blacksquare$