Project Euler 21 : Amicable Numbers

from math import ceil, sqrt
fsum=0
def div (n):
    sum=1
    #speed trick, lowest divisor of a pair is always lower than sqrt(n), allows the program to run much faster
    for i in range (2,ceil(sqrt(n)),1):
        if n%i==0:
            sum=sum+i
            sum=sum+(n/i)
    return sum

def ami(n):
    x=div(n)
    y=div(x)
    if n==y and n!=x:
        return True
    else:
        return False

for i in range(1,10001,1):
    if ami(i)==True:
        fsum=fsum+i
print(fsum)