MathDB

For a positive integer

n

, denote by

\tau(n)

the number of positive integer divisors of

n

, and denote by

\phi(n)

the number of positive integers that are less than or equal to

n

and relatively prime to

n

. Call a positive integer

n

\emph{good} if

\varphi (n) + 4\tau (n) = n

. For example, the number

44

is good because

\varphi (44) + 4\tau (44)= 44

.
Find the sum of all good positive integers

n

Problem Statement