def solve():
i = 1000
while True:
print i
a,b,c,d = factor(i), factor(i+1), factor(i+2), factor(i+3)
if distinctFact(a,b) and distinctFact(a,c) and distinctFact(a,d) and distinctFact(b,c) \
and distinctFact(b,d) and distinctFact(c,d):
return i
else:
i += 1
def solve():
i = 1000
while True:
print i
a, b, c, d = factor(i), factor(i + 1), factor(i + 2), factor(i + 3)
if distinctFact(a,b) and distinctFact(a,c) and distinctFact(a,d) and distinctFact(b,c) \
and distinctFact(b,d) and distinctFact(c,d):
return i
else:
i += 1
def main():
prev_val = False
for i in range(2, 10000):
max_val, max_ind = S2(i)
if max_val != prev_val:
print i, max_val, max_ind, factor(max_ind), is_square(max_ind)
prev_val = max_val
def E70():
res = 0
min_res = 100
min_i = 100
p_set = []
for i in range (3, MAXNUM, 2):
if is_prime(i) == True:
continue
p_set = factor(i)
if len(p_set) != 2:
continue
if int(p_set[0][1])!=1 or int(p_set[1][1])!=1:
continue
# [(421, 1), (571, 1)] <- both are 1
cnt = i - (int(p_set[0][0])+int(p_set[1][0])-1)
if is_perm(i, cnt) == False:
continue
res = float(i)/float(cnt)
if min_res >= res:
min_res = res
min_i = i
#print min_res, min_i, cnt, (1, p_set[0][0], p_set[1][0], i)
print "result", min_res, min_i
return 0
def num_divisors(x):
"""returns the number of divisors of x"""
l = factor(x)
divisors = 1
for exp in l:
divisors *= exp[1]+1
return divisors
def E70():
res = 0
min_res = 100
min_i = 100
p_set = []
for i in range(3, MAXNUM, 2):
if is_prime(i) == True:
continue
p_set = factor(i)
if len(p_set) != 2:
continue
if int(p_set[0][1]) != 1 or int(p_set[1][1]) != 1:
continue
# [(421, 1), (571, 1)] <- both are 1
cnt = i - (int(p_set[0][0]) + int(p_set[1][0]) - 1)
if is_perm(i, cnt) == False:
continue
res = float(i) / float(cnt)
if min_res >= res:
min_res = res
min_i = i
#print min_res, min_i, cnt, (1, p_set[0][0], p_set[1][0], i)
print "result", min_res, min_i
return 0
def totient(n): F = factor(n) factors = zip(*F)[0] val = 1 for num in factors: val *= (num-1)/float(num) val *= (n) return int(val)
def brute_force(num_div):
n = 1
while True:
factorization = factor(n)
#print factorization
num_factors = product([(x[1] + 1) for x in factorization])
#print num_factors
if num_factors == num_div:
return num
n += 1
def main(limit): num = 1 vals = [] while num < limit: val = 2*num**2-1 vals.append(val) if not is_prime(val): print val, factor(val) num += 1 return vals
def d(n):
div_cache = cache[n]
if div_cache != -1:
return div_cache
else:
factorization = factor(n)
div = 1
for val in factorization:
div *= (val[1] + 1)
cache[n] = div
return div
def D3(k):
target = 20010
prod = 1
divisors = get_divisors(factor(k))
for d in divisors:
if is_prime(d+1):
prod *= (d+1)
if prod > target:
return False
return prod
def get_divisors(n):
factors = factor(n)
nfactors = len(factors)
f = [0] * nfactors
while True:
yield reduce(lambda x, y: x * y,
[factors[x][0]**f[x] for x in range(nfactors)], 1)
i = 0
while True:
f[i] += 1
if f[i] <= factors[i][1]:
break
f[i] = 0
i += 1
if i >= nfactors:
return
def rad(x):
factors = factor(x)
prod = 1
for item in factors:
prod *= item[0]
return prod
<p>Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?</p>
</div><br />
<br /></div>
"""
from Euler import is_prime
# best
from Euler import factor
ci = 1
nf = 4 # number of distinct factors
ns = 4 # number of consecutive integers
n = 2 * 3 * 5 * 7 # starting candidate for search
while ci != ns:
n += 1
if len(factor(n)) == nf:
ci += 1
print n, ci, nf, factor(n)
else:
ci = 0
print "Project Euler 47 Solution =", n - nf + 1
# slow
'''
ps = [ ]
i = 0
num = 1
while (i != 200):
if (is_prime(num) == True):
i+=1
def get_exps(n):
return list(x[1] for x in factor(n))
</div><br />
<br /></div>
"""
from Euler import is_prime
# best
from Euler import factor
ci = 1
nf = 4 # number of distinct factors
ns = 4 # number of consecutive integers
n = 2*3*5*7 # starting candidate for search
while ci != ns:
n += 1
if len(factor(n)) == nf:
ci += 1
print n, ci, nf, factor(n)
else: ci = 0
print "Project Euler 47 Solution =", n-nf + 1
# slow
'''
ps = [ ]
i = 0
num = 1
while (i != 200):
if (is_prime(num) == True):
i+=1
ps.append(num)
def sopf(p):
sum=0
for i in factor(p):
sum+=i[0]
return sum
#!/usr/bin/python
#
# math from: http://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler.27s_product_formula
#
from Euler import factor
from operator import mul
print '\nAnswer: {0}'.format(max([(reduce(mul, map(lambda p:1-1/float(p), map(lambda t: t[0], factor(n))))**-1, n) for n in range(2, 10**6+1)]))
def uniq_f(n): return [t[0] for t in factor(n)]