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Sum of Digit Sum
Suppose, $S(a)$ is the sum of the digits in $a$. Let $F(n)$ denote the set of integers from $1$ to $1000$ such that $S(n\cdot a) = n \cdot S(a)$. Find- $$\large \sum_{i=1}^{63} |F(i)|$$
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Suppose, $S(a)$ is the sum of the digits in $a$. Let $F(n)$ denote the set of integers from $1$ to $1000$ such that $S(n\cdot a) = n \cdot S(a)$. Find- $$\large \sum_{i=1}^{63} |F(i)|$$
an22inkle