def juggler_sequence(number: int) -> list[int]:
    if not isinstance(number, int):
        raise TypeError(f"Input value of [number={number}] must be an integer")
    if number < 1:
        raise ValueError(f"Input value of [number={number}] must be a positive integer")
    sequence = [number]
    while number != 1:
        if number % 2 == 0:
            number = math.floor(math.sqrt(number))
        else:
            number = math.floor(
                math.sqrt(number) * math.sqrt(number) * math.sqrt(number)
            )
        sequence.append(number)
    return sequence