## Common factors between two sequences

### Problem 489

Let `G`(`a`, `b`) be the smallest non-negative integer `n` for which gcd(`n`^{3} + `b`, (`n` + `a`)^{3} + `b`) is maximized.

For example, `G`(1, 1) = 5 because gcd(`n`^{3} + 1, (`n` + 1)^{3} + 1) reaches its maximum value of 7 for `n` = 5, and is smaller for 0 ≤ n < 5.

Let `H`(`m`, `n`) = ∑ `G`(`a`, `b`) for 1 ≤ `a` ≤ `m`, 1 ≤ `b` ≤ `n`.

You are given `H`(5, 5) = 128878 and `H`(10, 10) = 32936544.

Find `H`(18, 1900).