Can we classify the solutions of $\ 2n-\sigma(n)=-12\ $ completely?

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A number-13 phenomenon

contains the equation $$ 2n-\sigma(n)=-12 $$ where $\ \sigma(n)\ $ is the sum of the divisors of $\ n\ $ including $\ n\ $.

There are two families of solutions :

• If $\ p>3\ $ is prime , then $\ 6p\ $ is a solution
• If $\ p=2^k-13\ $ , $\ k\ $ integer , is prime , then $\ 2^{k-1}\cdot p\ $ is a solution

The only solution upto $\ 10^9\ $ that fits in neither family, is $\ n=54\ $.

Is the list complete with the two families and the additional solution $\ 54\ $ ?