def lcm(a, b):
if a and b:
da = list(decompose(abs(a)))
db = list(decompose(abs(b)))
merge = da
for d in da:
if d in db: db.remove(d)
merge += db
return reduce(operator.mul, merge, 1)
return 0
def lcm(a, b):
if a and b:
da = list(decompose(abs(a)))
db = list(decompose(abs(b)))
merge= da
for d in da:
if d in db: db.remove(d)
merge += db
return reduce(operator.mul, merge, 1)
return 0
def lcm(a, b):
mul = int.__mul__
if a and b:
da = list(decompose(abs(a)))
db = list(decompose(abs(b)))
merge= da
for d in da:
if d in db: db.remove(d)
merge += db
return reduce(mul, merge, 1)
return 0
def decompose_me(n):
return imap(
lambda (k, v): (k, reduce(lambda x, y: x+1, v, 0)),
groupby(
decompose(n)
)
)
def euler_totient_float(n):
result = n
for p in set(decompose(n)):
result *= 1 - 1/float(p)
return int(round(result))
def almostprime(n, k=2):
d = decompose(n)
try:
terms = [next(d) for i in range(k)]
return reduce(int.__mul__, terms, 1) == n
except:
return False
def euler_totient_float(n):
result = n
for p in set(decompose(n)):
result *= 1 - 1 / float(p)
return int(round(result))
def almostprime(n, k=2):
d = decompose(n)
try:
terms = [next(d) for i in range(k)]
return reduce(int.__mul__, terms, 1) == n
except:
return False
def euler_totient(n):
result = Decimal(n)
for p in set(decompose(n)):
factor = 1 - 1 / Decimal(p)
result *= factor
return int(result)
def euler_totient(n):
result = Decimal(n)
for p in set(decompose(n)):
factor = 1 - 1/Decimal(p)
result *= factor
return int(result)
def find_euler_perms(n):
min_ratio = 100000
min_ratio_n = 1
for x in range(2,n - 1):
factors = list(decompose(x))
if len(factors) == 2:
p = factors[0]
q = factors[1]
prime_factor_ratio = (1 - 1/float(p))*(1 - 1/float(q))
# totient = euler_totient_float(x)
totient = int(round(x*prime_factor_ratio))
ratio = x / float(totient)
if is_permutation(x,totient) and ratio < min_ratio:
min_ratio = ratio
min_ratio_n = n
print "Got new min ratio n " + str(x) + " for ratio " + str(ratio)
def find_euler_perms(n):
min_ratio = 100000
min_ratio_n = 1
for x in range(2, n - 1):
factors = list(decompose(x))
if len(factors) == 2:
p = factors[0]
q = factors[1]
prime_factor_ratio = (1 - 1 / float(p)) * (1 - 1 / float(q))
# totient = euler_totient_float(x)
totient = int(round(x * prime_factor_ratio))
ratio = x / float(totient)
if is_permutation(x, totient) and ratio < min_ratio:
min_ratio = ratio
min_ratio_n = n
print "Got new min ratio n " + str(x) + " for ratio " + str(
ratio)
def semiprime(n):
d = decompose(n)
try:
return next(d) * next(d) == n
except:
return False
def semiprime(n):
d = decompose(n)
try:
return next(d) * next(d) == n
except StopIteration:
return False
def semiprime(n):
d = decompose(n)
try:
return next(d) * next(d) == n
except:
return False
def get_divisor_count(number):
decomp = list(decompose(number))
return functools.reduce(operator.mul, [decomp.count(prime) + 1 for prime in unique(decomp)], 1)
