First note that if $n=s*2^r$ where $s$ is odd then $n=3t(n)+5r(n)$ so $8s \geq n >3s$. Thus $r$ can be $2$ or $3$. Case $1$: $r=3$. Thus $s=t(n)=r(n)$ so $s$ is prime. So all numbers of the form $8p$ work where $p$ is an odd prime. Case $2$: $r=2$. Thus $s=t(n)$ and $r(n)=\frac{s}{5}$. Since $5$ is prime, $s$ is of the form $5p$ where $p$ is an odd prime less than or equal to $5$. In short, $s$ is either $15$ or $25$. So the solutions are: $60,100,8p$ where $p$ is an odd prime.