Let S be the set of integer triplets (a, b, c) with 1 \leq a \leq b \leq c that satisfy a+b+c=77 and:
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{5}
What is the value of the \operatorname{sum} \sum_{(a, b, c) \in S} a \cdot b \cdot c?
Let S be the set of integer triplets (a, b, c) with 1 \leq a \leq b \leq c that satisfy a+b+c=77 and:
What is the value of the \operatorname{sum} \sum_{(a, b, c) \in S} a \cdot b \cdot c?