def m_search(n,k,m=1,phi=1,lowerInd=0):
global primes,mask,pcap
s = 0
if k == 0:
M = m*phi-phi+m
bnd = int(M**.25)
pi = bisect_right(primes,n/m)
if n/m > pcap:
f = shanks_factorize(M,primes[:15])
for d in divisors([[bas,f[bas]] for bas in f]):
q,r = divmod(d-phi,m-phi)
if r == 0 and q > primes[lowerInd] and q*m <= n and is_prime(q,pcap-1,mask):
if (q*m-1) % (q*m - (q-1)*phi) == 0:
s += q*m
else:
for q in primes[lowerInd+1:pi+1]:
if q*m <= n and (q*m-1) % (q*m - (q-1)*phi) == 0:
s+= q*m
# print q*m,q,m
return s
bound = int((n/m)**(1./(k+1)))
i=lowerInd+1
for i,p in enumerate(primes[lowerInd+1:],lowerInd+1):
if p > bound:
break
else:
s += m_search(n,k-1,m*p,phi*(p-1),i)
return s
def find_pairs(n):
global primes,mask
s = 0
pairs = {}
for p in primes[1:]:
num = p**2-p+1
f = shanks_factorize(num,primes[:15])
for k in divisors([[bas,f[bas]] for bas in f] ):
q = num/k - p + 1
if q > 0 and q > p and q*p <= n and is_prime(q,pcap-1,mask):
s += p*q
# print p,q
if p not in pairs:
pairs[p] = [q]
else:
pairs[p].append(q)
print "Sum over semi-primes %d" % s
#now do backtracking pair-combos
for p1 in pairs:
for p2 in pairs[p1]:
s += cores_backtrack(n/p1/p2,pairs,[p1,p2])
return s
#f = floor, r = room
def P(f,r):
if f == 1:
return r*(r+1) / 2
k = (r-1)/2
b = [(f*f) / 2]
nextSquare = 2*(f/2)+1
b.append((nextSquare)**2 - b[0])
b.append((nextSquare+1)**2 - b[1])
if r <= 3:
return b[r-1]
else:
if not r%2:
a = b[2] - b[0] + 2
return b[1] + pe.arithmetic(a,4,k)
else:
a = b[2] - b[0]
return b[0] + pe.arithmetic(a,4,k)
n = 71328803586048
factors = [(2,27), (3,12)]
s = 0
for f in pe.divisors(factors):
s = (s + P(f,n/f)) % mod
print s