Aliquot divisors are all the divisors of a number except the number itself. The product of the Aliquot divisors of a number is somtimes equal to the square of the number. The Aliquot divisors of of 12 are 1 ,2 ,3 ,4 ,6. Their product,1x2x3x4x6=144=12*2 is the smallest number with this property. Three other numbers less than 30 have this property. Find two of them.

Question

Aliquot divisors are all the divisors of a number except the number itself. The product of the Aliquot divisors of a number is somtimes equal to the square of the number. The Aliquot divisors of of 12 are 1 ,2 ,3 ,4 ,6. Their product,1x2x3x4x6=144=12*2 is the smallest number with this property. Three other numbers less than 30 have this property. Find two of them.

Answer 1

If you notice that numbers with the required property has two pairs of factors, for example, for 12, we have

2*6, 4*3.
Which means that numbers divisible by 4 are more likely to have this property.
Can you find them?

Answer 2

To find the two numbers less than 30 that have the property where the product of their Aliquot divisors is equal to the square of the number, we will iterate through the numbers and calculate their Aliquot divisors' product.

Here's how you can do it:

1. Start by defining a function to calculate the Aliquot divisors of a given number. The function should iterate from 1 to (n/2) and check if each number evenly divides the given number. If it does, add it to a list of divisors.

2. Iterate through the numbers less than 30 and calculate their Aliquot divisors' product using the defined function. Check if the product is equal to the square of the number. If it is, store the number as a candidate.

3. Continue iterating until you find at least two numbers that satisfy the property.

Here's a Python code snippet to help you find the two numbers:

```python
def get_aliquot_divisors(n):
divisors = []
for i in range(1, n // 2 + 1):
if n % i == 0:
divisors.append(i)
return divisors

candidates = []
for num in range(1, 30):
aliquot_product = 1
divisors = get_aliquot_divisors(num)
for divisor in divisors:
aliquot_product *= divisor
if aliquot_product == num ** 2:
candidates.append(num)
if len(candidates) == 2:
break

print("Two numbers less than 30 with the specified property:", candidates)
```

When you run this code, it will output the two numbers less than 30 that have the property where the product of their Aliquot divisors is equal to the square of the number.