Divisor Sum of 1257

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {1257} = 1680$

Proof

We have that:

$1257 = 3 \times 419$

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

Hence:

\(\ds \map {\sigma_1} {1257}\)

\(=\)

\(\ds \paren {3 + 1} \paren {419 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 4 \times 420\)

\(\ds \)

\(=\)

\(\ds 2^2 \times \paren {2^2 \times 3 \times 5 \times 7}\)

\(\ds \)

\(=\)

\(\ds 1680\)

$\blacksquare$