let $P(n) = n^4 + an^3 + bn^2 + cn$
$M(a,b,c)$ returns largest $m$ that divides $P(n)$ for all n
then let function $S(N)$ return the sum of all $M(a,b,c)$ for $1 \le a,b,c \le N$
I don't need anyone to solve this for me but just point me in the right direction. I am trying to understand a simpler way to calculate $S(N)$ so I don't have to actually process every single combination of a,b, and c but I am having trouble finding patterns to take advantage of on a broad scale.
So far I know from trying all sorts of values that M(a,b,c) tends to return values of form $2^i \times 3^j$ where $i,j\ge0$.