def factors(num, primes = None):
factors = []
if num > 3:
buf = num
if primes:
fcandidates = [prime for prime in primes if prime < (num/2) +1]
else:
fcandidates = prime_sieve((num/2)+1)
for candidate in fcandidates:
cond = True
while cond:
r = buf % candidate
if r == 0:
factors.append(candidate)
buf /= candidate
elif buf == 1:
break
else:
cond = False
return factors
def main():
primes = prime_sieve(1000)
minns = []
for k in range(2, 200):
cond = True
n = 2
while cond:
if n in primes:
n += 1
continue
combs = reductions_full(n)
for item in combs:
# pad with ones
s = sum(item) + k - len(item)
pr = prod(item)
# print n, pr, s
if s == pr:
print("K: %d, N: %d, pr: %d, s: %d" % (k, n, pr, s))
if pr not in minns:
minns.append(pr)
cond = False
break
n += 1
print sum(minns)
