Poulet Numbers which are also Magic Constant for Magic Square

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Theorem

The sequence of Poulet numbers which are also the magic constant of a magic square begins:

$1105, 2465, \ldots$


Proof

From the sequence of Poulet numbers, these are Poulet numbers:

$1105, 2465, \ldots$

Then we have:

\(\ds 1105\) \(=\) \(\ds \dfrac {13 \paren {13^2 + 1} } 2\) so $1105$ is the magic constant of the order $13$ magic square
\(\ds 2465\) \(=\) \(\ds \dfrac {17 \paren {17^2 + 1} } 2\) so $2465$ is the magic constant of the order $17$ magic square