def problem21(n):
result = 0
for a in xrange(2, n + 1):
b = PrimeMethods.sopdf(a, 1) - a
a_prime = PrimeMethods.sopdf(b, 1) - b
if a == a_prime and a != b:
#print((a, b))
result += a
return result
def is_abundant(n):
if n < 12:
return False
spd = PrimeMethods.sopdf(n, 1) - n
return spd > n
