How can I find primes multiplied by powers of two in a Python range?

Here is a beginner-friendly version:

```python
def is_prime(n):
if n < 2:
return False
for divisor in range(2, int(n ** 0.5) + 1):
if n % divisor == 0:
return False
return True

def is_special(n):
while n % 2 == 0:
n //= 2
return n == 1 or is_prime(n)

start = int(input("Start: "))
end = int(input("End, inclusive: "))

for number in range(start, end + 1):
if is_special(number):
print(number)
```

The `+ 1` makes the ending value inclusive. Without it, Python's `range` stops just before `end`.

You can also think of this as removing every factor of two and checking what remains. Bit shifting can do the same thing, but repeated integer division is much easier to understand when you’re learning. Also, 10 is 5×2^1, not 5×2^2; 8 is 2^3, and 16 is 2^4.

A useful way to test this is to repeatedly divide the number by 2 while it is even. Once that is finished, the remaining value is odd. The original number has the desired form if that remaining value is 1 or a prime number. For example, 40 becomes 20, then 10, then 5, so it qualifies because 5 is prime. You can put that logic in an `is_special` function and use it while looping through the range.