Sequences of 4 Consecutive Integers with Rising Divisor Sum

Theorem

The following ordered quadruples of consecutive integers have divisor sum values which are strictly increasing:

$61, 62, 63, 64$

$73, 74, 75, 76$

Proof

\(\ds \map {\sigma_1} {61}\)

\(=\)

\(\ds 62\)

Divisor Sum of Prime Number: $61$ is prime

\(\ds \map {\sigma_1} {62}\)

\(=\)

\(\ds 96\)

$\sigma_1$ of $62$

\(\ds \map {\sigma_1} {63}\)

\(=\)

\(\ds 104\)

$\sigma_1$ of $63$

\(\ds \map {\sigma_1} {64}\)

\(=\)

\(\ds 127\)

$\sigma_1$ of $64$

\(\ds \map {\sigma_1} {73}\)

\(=\)

\(\ds 74\)

Divisor Sum of Prime Number: $73$ is prime

\(\ds \map {\sigma_1} {74}\)

\(=\)

\(\ds 114\)

$\sigma_1$ of $74$

\(\ds \map {\sigma_1} {75}\)

\(=\)

\(\ds 124\)

$\sigma_1$ of $75$

\(\ds \map {\sigma_1} {76}\)

\(=\)

\(\ds 140\)

$\sigma_1$ of $76$

$\blacksquare$

Also see

• Sequences of 4 Consecutive Integers with Falling Divisor Sum

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $61$