|
|
@@ -0,0 +1,70 @@
|
|
|
+from math import sqrt
|
|
|
+
|
|
|
+def appendEs2Sequences(sequences,es):
|
|
|
+ result=[]
|
|
|
+ if not sequences:
|
|
|
+ for e in es:
|
|
|
+ result.append([e])
|
|
|
+ else:
|
|
|
+ for e in es:
|
|
|
+ result+=[seq+[e] for seq in sequences]
|
|
|
+ return result
|
|
|
+
|
|
|
+
|
|
|
+def cartesianproduct(lists):
|
|
|
+ return reduce(appendEs2Sequences,lists,[])
|
|
|
+
|
|
|
+def primefactors(n):
|
|
|
+ i = 2
|
|
|
+ while i<=sqrt(n):
|
|
|
+ if n%i==0:
|
|
|
+ l = primefactors(n/i)
|
|
|
+ l.append(i)
|
|
|
+ return l
|
|
|
+ i+=1
|
|
|
+ return [n]
|
|
|
+
|
|
|
+def factorGenerator(n):
|
|
|
+ p = primefactors(n)
|
|
|
+ factors={}
|
|
|
+ for p1 in p:
|
|
|
+ try:
|
|
|
+ factors[p1]+=1
|
|
|
+ except KeyError:
|
|
|
+ factors[p1]=1
|
|
|
+ return factors
|
|
|
+
|
|
|
+def divisors(n):
|
|
|
+ factors = factorGenerator(n)
|
|
|
+ divisors=[]
|
|
|
+ listexponents=[map(lambda x:k**x,range(0,factors[k]+1)) for k in factors.keys()]
|
|
|
+ listfactors=cartesianproduct(listexponents)
|
|
|
+ for f in listfactors:
|
|
|
+ divisors.append(reduce(lambda x, y: x*y, f, 1))
|
|
|
+ divisors.sort()
|
|
|
+ return divisors
|
|
|
+
|
|
|
+def is_square(apositiveint):
|
|
|
+ x = apositiveint // 2
|
|
|
+ seen = set([x])
|
|
|
+ while x * x != apositiveint:
|
|
|
+ x = (x + (apositiveint // x)) // 2
|
|
|
+ if x in seen: return False
|
|
|
+ seen.add(x)
|
|
|
+ return True
|
|
|
+
|
|
|
+def o2(n):
|
|
|
+ sumsq = 0
|
|
|
+ for factor in divisors(n):
|
|
|
+ sumsq += factor**2
|
|
|
+ return sumsq
|
|
|
+
|
|
|
+def main():
|
|
|
+ divsqsum = 0
|
|
|
+ for i in range(1,64000000):
|
|
|
+ if is_square(o2(i)):
|
|
|
+ divsqsum += o2(i)
|
|
|
+ print o2(i)
|
|
|
+ print divsqsum
|
|
|
+
|
|
|
+main()
|
