def slow():
"""
Use a generating function to retrieve partition of size k
and determine the smallest integer that satisfy sum(ak) = prod(ak)
EDIT: works but two slow (exponential time to compute the partitions)
"""
import IntegerPartitions
prod = lambda iterable: reduce(lambda x,y: x*y, iterable, 1)
s = set()
i = 2
for k in range(2,N+1):
#i = k
while True:
for p in IntegerPartitions.mckay(i):
if len(p) != k: continue
if prod(p) == i:
break
if prod(p) == i:
break
i += 1
print "found", i, k
s.add(i)
return sum(s)
def fixed_length_partitions(i,k): return IntegerPartitions.fixed_length_partitions(i,k)
