# Problem 542: Geometric Progression with Maximum Sum
Let S(k) be the sum of three or more distinct positive integers having
the following properties: No value exceeds k. The values form a
geometric progression. The sum is
maximal.S(4) = 4 + 2 + 1 = 7S(10) = 9 + 6 + 4 = 19S(12) = 12 + 6 + 3 = 21S(1000) = 1000 + 900 + 810 + 729 = 3439
Let \$T(n) = \\sum\_{k=4}\^n (-1)\^k S(k)\$.T(1000) = 2268 Find T(1017).