This one only took a couple of tries. The toughest part really is reading the directions carefully. First time through I missed the a does not equal b requirement. Surprisingly, this made a big difference in the final total.
from time import time
start_time= time()
print """Process started
----------"""
def d(n):
a = 0
for i in range(1, n):
if n%i == 0:
a = a + i
return a
sum = 0
for s in range(1, 10**4):
print s
if (d(d(s)) == s) and (d(s) != s):
sum = sum + s
print sum
end_time= time()
elapse_time= end_time - start_time
print '----------'
print elapse_time, 'seconds have passed'