def binom_dd(n, k):
out = []
ee = []
for x in range(1, k + 1):
out += mylib.find_dividers(n - x + 1)
if x < 2:
continue
ee += mylib.find_dividers(x)
# print("+", sorted(out),"\n-", sorted(ee))
for x in ee:
if x in out:
ix = out.index(x)
out = out[:ix] + out[ix + 1:]
return tuple(sorted(out))
def binom_dd(n, k):
out = []
ee = []
for x in range(1, k + 1):
out += mylib.find_dividers(n - x + 1)
if x < 2:
continue
ee += mylib.find_dividers(x)
# print("+", sorted(out),"\n-", sorted(ee))
for x in ee:
if x in out:
ix = out.index(x)
out = out[:ix] + out[ix + 1 :]
return tuple(sorted(out))
def solve():
result = 0
f0 = 3 / 7
print(3, '/', 7, '=', f0)
print('-' * 79)
best_result = (1, 1, 1, 1, [], [])
for x in range(1000000, 1, -1):
n = math.floor(f0 * x)
f = n / x
d = f0 - f
if d and d < best_result[2]:
best_result = (n, x, d, f, mylib.find_dividers(n, distinct=True), mylib.find_dividers(x, distinct=True))
print(best_result)
print('-' * 79)
print(best_result)
return best_result[0]
def solve():
result = 0
f0 = 3 / 7
print(3, '/', 7, '=', f0)
print('-' * 79)
best_result = (1, 1, 1, 1, [], [])
for x in range(1000000, 1, -1):
n = math.floor(f0 * x)
f = n / x
d = f0 - f
if d and d < best_result[2]:
best_result = (n, x, d, f, mylib.find_dividers(n, distinct=True),
mylib.find_dividers(x, distinct=True))
print(best_result)
print('-' * 79)
print(best_result)
return best_result[0]
def get_totient(n):
dd = mylib.find_dividers(n, distinct=True)
phi = n - 1
print(dd)
for d in dd:
if d == n:
continue
phi -= n / d - 1
print(n, phi)
return n / phi
def count_fractions_for_denominator(d):
dd = mylib.find_dividers(d, distinct=True)
if len(dd) == 1:
if dd[0] == d:
return d - 1
return int((dd[0] - 1) * d / dd[0])
out = d
for x in dd:
out = (x - 1) * out / x
return out
def count_fractions_for_denominator(d):
dd = mylib.find_dividers(d, distinct=True)
if len(dd) == 1:
if dd[0] == d:
return d - 1
return int((dd[0] - 1) * d / dd[0])
out = d
for x in dd:
out = (x - 1) * out / x
return out
def find(n):
print(n)
r = dict()
for i in range(1, n + 1):
dd = mylib.find_dividers(i, distinct=True)
if len(dd) != 2:
continue
ix = 'x'.join([str(x) for x in dd])
r[ix] = i
print(i, ix)
return sum([r[x] for x in r])
def find(n):
print(n)
r = dict()
for i in range(1, n + 1):
dd = mylib.find_dividers(i, distinct=True)
if len(dd) != 2:
continue
ix = 'x'.join([str(x) for x in dd])
r[ix] = i
print(i, ix)
return sum([r[x] for x in r])
def solve():
a = 0
for a in range(1000, 1000000):
d = mylib.find_dividers(a, distinct=True)
if len(d) < 4:
continue
c = False
e = []
for b in range(a + 1, a + 4):
dd = mylib.find_dividers(b, distinct=True)
if len(dd) < 4:
c = True
break
e.append(str(b) + ' ' + str(dd))
if len(e) > 2:
print(a, d, e)
if not c:
break
return a
def make_primes(self):
self.rr = []
for x in self.ss:
print(x, ':')
for y in (1, 3, 7, 9):
r = 10 * x + y
if r in self.pp:
# if mylib.is_prime(r):
print('+', r, 'is prime')
self.rr.append(r)
else:
print('-', r, 'is NOT prime', mylib.find_dividers(r))
return self
def count_fractions_old(v):
for i in range(0, v + 1):
if len(dividers_hash) <= i:
dividers_hash.append(set(mylib.find_dividers(i, distinct=True)))
print('hash constructed to', len(dividers_hash) - 1)
out = 0
for d in range(2, v + 1):
for n in range(1, d):
r = is_proper_fraction(n, d)
out += r
if not d % 1000 and not n % 1000:
print(n, '/', d, out)
# print(n, '/', d, '=', r)
return out
def count_fractions_old(v):
for i in range(0, v + 1):
if len(dividers_hash) <= i:
dividers_hash.append(set(mylib.find_dividers(i, distinct=True)))
print('hash constructed to', len(dividers_hash) - 1)
out = 0
for d in range(2, v + 1):
for n in range(1, d):
r = is_proper_fraction(n, d)
out += r
if not d % 1000 and not n % 1000:
print(n, '/', d, out)
# print(n, '/', d, '=', r)
return out
def is_hamming_brute(n):
t = mylib.totient(n)
dd = mylib.find_dividers(t, distinct=True)
# print(n, t, max(dd))
return max(dd) < 6
return out
def ww_to_n(w_list):
out = 1
for x in w_list:
out *= w_list[x] + 1
return out
m = 0
s = 2 * 3 * 5 * 7
for n in range(s, 1000, s):
if mylib.is_prime(n):
continue
pd = mylib.find_dividers(n)
if len(pd) < 4:
continue
dd = mylib.find_composite_dividers(n)
print(n, len(dd), dd)
ss = set()
for a in dd:
for b in dd:
if b > a:
continue
if mylib.find_gcd(a, b) > 1:
continue
z = a + b
x = round(n * z / b)
y = round(n / a) * z
print(a, b, x, y, x * y / (x + y))
def is_proper_fraction(n, d):
return n and n < d and not \
len(set(mylib.find_dividers(n, distinct=True)) & set(mylib.find_dividers(d, distinct=True)))
return out
def ww_to_n(w_list):
out = 1
for x in w_list:
out *= w_list[x] + 1
return out
m = 0
s = 2 * 3 * 5 * 7
for n in range(s, 1000, s):
if mylib.is_prime(n):
continue
pd = mylib.find_dividers(n)
if len(pd) < 4:
continue
dd = mylib.find_composite_dividers(n)
print(n, len(dd), dd)
ss = set()
for a in dd:
for b in dd:
if b > a:
continue
if mylib.find_gcd(a, b) > 1:
continue
z = a + b
x = round(n * z / b)
y = round(n / a) * z
print(a, b, x, y, x * y / (x + y))
def get_common_dividers():
return list(set(mylib.find_dividers(abs(self.n))).intersection(
set(mylib.find_dividers(self.d))))
def is_hamming_brute(n):
t = mylib.totient(n)
dd = mylib.find_dividers(t, distinct=True)
# print(n, t, max(dd))
return max(dd) < 6
