def allFactorSums(x):
if (x not in dict1):
if (pi.isPrime(x)):
return [(x, 1)]
else:
total1 = []
facts = pi.getFactors(x)[1:]
for i in facts:
for j in allFactorSums(x // i):
total1.append((i + j[0], 1 + j[1]))
total1.append((i + x // i, 2))
dict1[x] = frozenset(total1)
return dict1[x]
def allFactorSums(x): if(x not in dict1): if(pi.isPrime(x)): return [(x,1)] else: total1 = [] facts = pi.getFactors(x)[1:] for i in facts: for j in allFactorSums(x//i): total1.append((i+j[0],1+j[1])) total1.append((i+x//i,2)) dict1[x] = frozenset(total1) return dict1[x]
def isAbundant(x):
return x < sum(prime.getFactors(x))