Divisor Sum of 295

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {295} = 360$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$295 = 5 \times 59$

and so by definition is a semiprime whose prime factors are distinct.

Hence:

\(\ds \map {\sigma_1} {295}\)

\(=\)

\(\ds \paren {5 + 1} \paren {59 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 6 \times 60\)

\(\ds \)

\(=\)

\(\ds \paren {2 \times 3} \times \paren {2^2 \times 3 \times 5}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3^2 \times 5\)

\(\ds \)

\(=\)

\(\ds 360\)

$\blacksquare$