Let $$Y = (\textbf{a})\cdot x_1 + (\textbf{a}+1)\cdot x_2 + (\textbf{a}+2)\cdot x_3 + (\textbf{a}+3)\cdot x_4 + . . . + (\textbf{a}+n)\cdot x_n$$
Where $x_1,x_2,x_3.... x_n$ are all positive integers $(\ge 0), n\ge 1$ and $a\ge1$.
NOTE: $x_1,x_2,x_3,... ,x_n$ can be any positive integers $(\ge0)$ and must not be distinct.
Given the value of $\textbf{a}$ count all possible values $Y\ge 1$ where there are no possible values of $x_1,x_2,x_3,... ,x_n$.
I just thought about this problem and I have been trying to think of a solution to this problem but all I could come up with is trying every possible value. Please help me solve.