Integers whose Ratio between Sigma and Phi is Square

From ProofWiki
Jump to navigation Jump to search

Theorem

The sequence of integers whose $\sigma$ value divided by its Euler $\phi$ value is a square begins:

$1, 30, 105, 248, 264, 714, \ldots$



Proof


\(\displaystyle \map \phi {714}\) \(=\) \(\displaystyle 192\) Euler Phi Function of 714
\(\displaystyle \map \sigma {714}\) \(=\) \(\displaystyle 1728\) Sigma of 714
\(\displaystyle \map \sigma {714} / \map \phi {714}\) \(=\) \(\displaystyle 1728 / 192\)
\(\displaystyle \) \(=\) \(\displaystyle 9\)
\(\displaystyle \) \(=\) \(\displaystyle 3^2\)



Sources