A perfect square is an integer that can be expressed as the product of two equal

Question

A perfect square is an integer that can be expressed as the product of two equal integers. For example, 4 = 22 is a perfect square. An integer n is called primitive if it is divisible by no perfect square other than 1. For example, 15 is primitive but 12 is not, as 12 is divisible by 4 = 22 (a perfect square).

Write a program to find the largest even primitive integer n < t.

def factor(n):
#Primes and Exponents(pae)
pae = []
for k in range(2, math.ceil(n ** 0.5)):
if n % k == 0:
exponent = 1
while n % (k ** exponent) == 0:
exponent += 1
pae.append([k, exponent-1])
n = n // (k ** (exponent-1))
if n != 1:
pae.append([n,1])   
return pae

def Isprimitive(n):
pae = factor(n)
for pair in pae:
if pair[1] != 1:
return False
else:
return True

def largestEvenPrimitive(n):
if n % 2 == 1:
n = n - 1
while (True):
if Isprimitive(n):
return n
else:
n = n - 2

print(largestEvenPrimitive(100))

this code prints 98, but I'm pretty sure is incorrect since 98 = 2 * 72.

Does this code address the question properly? is 98 the right output or can any changes be made to make it correct (if is not )?

Thank you  

Explanation / Answer

def check_primitive(n):
i=2
while(i<n):
k=i**i
if(n%k==0):#if divisible by perfect squre
return False
i+=1
return True
def Largest_even_primitive(t):
t-=1
while(t>1):
if(t%2==0):#check whether t is even or odd
if(check_primitive(t)):#if even then checking whether it is primitive or not
return t#returning the largest even primitive less than t
t-=1
s = int(input("Enter a number:"))
r = Largest_even_primitive(s)
print(r)

output:

Enter a number:5
2
>>> ================================ RESTART ================================
>>>
Enter a number:15
14
>>>

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