def find_by_k(self):
"""
a = 3k - 1
b = k
c = 8 * k - 3
:return:
"""
self.triplets = []
for bk in range(1, self.get_max_q()):
ck = (8 * bk - 3)
ak = 3 * bk - 1
sq_d = self.get_square_dividers(ck)
if ak + bk + ck > self.limit:
if mylib.is_prime(ck) and not len(sq_d):
continue
m0 = mylib.mult(sq_d)
b0 = bk * m0
c0 = int(ck / m0 / m0)
if c0 > self.limit - ak - 1:
continue
b_limit = self.limit - ak - c0
bm_bm = [(x, int(b0 / x) ** 2) for x in mylib.find_composite_dividers(b0, b_limit)]
for bm in bm_bm:
b = bm[0]
c = c0 * bm[1]
if ak + b + c > self.limit:
continue
t = [ak, b, c]
self.triplets.append(t)
print(t, len(self.triplets))
continue
return self
def find_by_k(self):
"""
a = 3k - 1
b = k
c = 8 * k - 3
:return:
"""
self.triplets = []
for bk in range(1, self.get_max_q()):
ck = (8 * bk - 3)
ak = 3 * bk - 1
sq_d = self.get_square_dividers(ck)
if ak + bk + ck > self.limit:
if mylib.is_prime(ck) and not len(sq_d):
continue
m0 = mylib.mult(sq_d)
b0 = bk * m0
c0 = int(ck / m0 / m0)
if c0 > self.limit - ak - 1:
continue
b_limit = self.limit - ak - c0
bm_bm = [(x, int(b0 / x)**2)
for x in mylib.find_composite_dividers(b0, b_limit)]
for bm in bm_bm:
b = bm[0]
c = c0 * bm[1]
if ak + b + c > self.limit:
continue
t = [ak, b, c]
self.triplets.append(t)
print(t, len(self.triplets))
continue
return self
def find_2mn(a):
out = []
if a % 2:
return out
dd = mylib.find_composite_dividers(a // 2)
_dd = dd[::-1]
l = len(dd)
# print(a, dd)
for i in range(l // 2):
d = _dd[i]**2 - dd[i]**2
if d > 2 * a:
continue
t = (a, d)
out.append(t)
return out
def find_2mn(a):
out = []
if a % 2:
return out
dd = mylib.find_composite_dividers(a // 2)
_dd = dd[::-1]
l = len(dd)
# print(a, dd)
for i in range(l // 2):
d = _dd[i] ** 2 - dd[i] ** 2
if d > 2 * a:
continue
t = (a, d)
out.append(t)
return out
def solve():
m = 100000000
data = [2]
for a in range(6, m, 4):
if not mylib.is_prime(a + 1) or not mylib.is_prime(a / 2 + 2):
continue
dd = mylib.find_composite_dividers(a)
if len(dd) % 2:
continue
# print(a, dd)
all_primes = True
for i in range(2, len(dd) // 2):
b = dd[i] + dd[len(dd) - i - 1]
all_primes = all_primes and mylib.is_prime(b)
# print(' ', dd[i], dd[len(dd) - i - 1], b, all_primes)
if not all_primes:
break
if all_primes:
print(a, dd)
data.append(a)
# print(data)
return sum(data)
else:
# print(x, '-', 'prime, 4k+1: impossible')
continue
if x % 4 == 1:
# print(x, '-', '(2k+1)(2(k+2p) + 1): impossible')
continue
if x % 4 == 2:
# print(x, '-', '2(2k+1): impossible')
continue
if x % 4 == 3:
# print(x, '-', '(2k+1)(2(k+2p+1)+1): at least 2 ways')
continue
if x % 16 and not x % 8:
# print(x, '-', '8(2k+1): impossible')
continue
dd = mylib.find_composite_dividers(x)
min_a = (x / 3)**0.5
rr = []
for i in range(len(dd)):
a = dd[i]
if a <= min_a:
continue
z = dd[-1 - i]
s = a + z
if s % 4:
continue
b = int(s / 4)
pr = (x + b, x, x - b)
rr.append(pr)
if len(rr) > 1:
break
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))
ss.add((min(x, y), max(
x,
y,
uu = []
for t in ttb:
u = (t[0], t[1] + t[2])
if u not in uu:
uu.append(u)
y = 0
uu1 = []
stored_tt = dict()
for a in range(1, M + 1):
clean_tt = find_mm_nn(a) + find_2mn(a)
stored_tt[a] = clean_tt
tt = clean_tt[:]
dd = mylib.find_composite_dividers(a)
for d in dd:
if d < 3 or d == a:
continue
if d in stored_tt:
# print(a, 'stored', stored_tt[d])
for t in stored_tt[d]:
t1 = (a, t[1] * a // d)
if t1 not in tt:
# print(a, ' <- ', t1)
tt.append(t1)
# tt += [x for x in stored_tt[d]]
uu1 += tt
if not len(tt):
continue
z = 0
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))
ss.add((min(x, y), max(x, y, )))
sl = len(ss)
import mylib
bb = {}
cc = {}
m = 10 ** 6 + 1
longest = (0,)
for a in range(m):
if a in cc:
continue
b = sum(mylib.find_composite_dividers(a)[:-1])
if a == b:
cc[a] = (), (b,)
continue
c = [a]
x = a
y = sum(mylib.find_composite_dividers(x)[:-1])
c_prefix = None
c_amicable = None
while y not in c:
# print(y)
if y in cc:
c_prefix = tuple(c) + cc[y][0]
c_amicable = cc[y][1]
break
c.append(y)
if y > m:
break
x = y
y = sum(mylib.find_composite_dividers(x)[:-1])