Divisor Sum of 6

Example of Divisor Sum of Integer

$\map {\sigma_1} 6 = 12$

where $\sigma_1$ denotes the divisor sum function.


Proof

We have that:

$6 = 2 \times 3$

Hence:

\(\ds \map {\sigma_1} 6\) \(=\) \(\ds \paren {2 + 1} \paren {3 + 1}\) Divisor Sum of Non-Square Semiprime
\(\ds \) \(=\) \(\ds 3 \times 4\)
\(\ds \) \(=\) \(\ds 2^2 \times 3\)
\(\ds \) \(=\) \(\ds 12\)

$\blacksquare$


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sigma function (sum function)
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