Problem #119
Minimum Cubes
We define f(x) = minimum number of positive perfect cubes that sum up to x.
For example,
f(2) = 2 (2 = 1^3 + 1^3)
f(9) = 2 (9 = 1^3 + 2^3)
f(17) = 3 (17 = 1^3 + 2^3 + 2^3)
Find \sum_{n=1}^{10^6} f(n).
We define f(x) = minimum number of positive perfect cubes that sum up to x.
For example,
f(2) = 2 (2 = 1^3 + 1^3)
f(9) = 2 (9 = 1^3 + 2^3)
f(17) = 3 (17 = 1^3 + 2^3 + 2^3)
Find \sum_{n=1}^{10^6} f(n).