4000 Followers Problem!

a!+b!+c!=a!b!\large a! + b! + c! = a! \cdot b!

If a,b,ca,b,c are nonnegative integers, then there are a finite number of solutions to the above equation. Let them be (a1,b1,c1),(a2,b2,c2),(a3,b3,c3),,(an,bn,cn)(a_1, b_1, c_1), (a_2, b_2, c_2), (a_3, b_3, c_3), \ldots, (a_n, b_n, c_n) in some order. Find the value of

n+i=1n(ai+bi+ci).n + \displaystyle \sum_{i=1}^n (a_i+b_i+c_i ).

(If n=0n = 0, then the sum is zero, so you should write 0 as the answer.)

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