def p073(N=12000):
retval = 0
for d in range(2,N+1):
total = p069.phi(d)
lowerthird = len([n for n in range(d/3+1) if numty.gcd(n,d) == 1])
retval += total/2-lowerthird
return retval
def uniques(N):
table = [[] for n in range(N+1)]
for k in range(1,N/12+1):
for mplusn in range(3,int(math.sqrt(N/k))+1,2):
for m in range(mplusn/2+1, mplusn):
p = 2*k*m*mplusn
if p > N:
break
if numty.gcd(m,mplusn) != 1:
continue
table[p].append((k,mplusn-m,m))
return [p for p in range(len(table)) if len(table[p]) == 1]
def uniques(N):
table = [[] for n in range(N + 1)]
for k in range(1, N / 12 + 1):
for mplusn in range(3, int(math.sqrt(N / k)) + 1, 2):
for m in range(mplusn / 2 + 1, mplusn):
p = 2 * k * m * mplusn
if p > N:
break
if numty.gcd(m, mplusn) != 1:
continue
table[p].append((k, mplusn - m, m))
return [p for p in range(len(table)) if len(table[p]) == 1]
def p127(N=120000):
rad_table = radtable(N)
a_table = sorted([(rad_table[a], a) for a in xrange(1, N)])
acc = 0
for c in xrange(N):
lim = c / rad_table[c]
for rad_a, a in a_table:
if rad_a > lim:
break
if a >= (c + 1) / 2:
continue
if numty.gcd(rad_table[a], rad_table[c]) == 1:
if rad_table[a] * rad_table[c - a] * rad_table[c] < c:
logger.debug('%d %d %d' % (a, c - a, c))
acc += c
return acc
def p127(N = 120000):
rad_table = radtable(N)
a_table = sorted([(rad_table[a], a) for a in xrange(1,N)])
acc = 0
for c in xrange(N):
lim = c/rad_table[c]
for rad_a, a in a_table:
if rad_a > lim:
break
if a >= (c+1)/2:
continue
if numty.gcd(rad_table[a],rad_table[c]) == 1:
if rad_table[a]*rad_table[c-a]*rad_table[c] < c:
logger.debug('%d %d %d' % (a, c-a, c))
acc += c
return acc
def lcm(a, b):
return a * b / numty.gcd(a, b)
def lcm(a,b):
return a*b/numty.gcd(a,b)