Sequences of 4 Consecutive Integers with Rising Divisor Sum
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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
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $61$