Divisors’ powers

First of all, if $n$ is odd the LHS will be odd and, because all the divisors of an odd number are odd too, and so their powers, the RHS will be the sum of two odds and a even so will be even; this is a nonsense. So $n$ must be even, so $d_2$ must be equal 2, so $n=2^2+d_4^4+2=d_4^4+6$ . Since $d_4$ divides $n$ and $d_4^4$ , it must divide 6 too; it can’t be equal 3, otherwise $2<d_3<3$ , so it must be equal 6; in conclusion $n=6^4+6=1302$ . It can be simply verified that 4 doesn’t divide 1302 so $d_2=2$ , $d_3=3$ and $d_4=6$