go = False
for i,(fact,num) in enumerate(f):
if c[i] < num:
c[i] += 1
m *= fact
go = True
break
m //= fact**num
c[i] = 0
def rad(a, b, c, R):
s = (a+b+c)/2
return ((s-a)*(s-b)*(s-c)/s) <= R*R
R = 1053779
divs = getdivs(4*R) # For factor()
I, J, K = 0, 0, 0
# Solve diophantine equation b^2+c^2-b*c=a^2 <=> (2b-c)^2-a^2=-3*c^2
for c in range(1, int(6*R/3**.5)):
for u in gendivs(divs, c):
v = -3*c*c//u
if (u-v)&3: continue
x, a = (u+v)//2, (u-v)//4
if (x+c)&1: continue
b = (x+c)//2
if a<b and rad(a,b,c,R):
I += 1
if I % 100000 == 0: print(I)
print(I)
f = list(c.items())
c, go, m = [0]*len(f), True, 1
while go:
yield m
go = False
for i,(fact,num) in enumerate(f):
if c[i] < num:
c[i] += 1
m *= fact
go = True
break
m //= fact**num
c[i] = 0
N, P, ok, done = 120000, defaultdict(set), set(), set()
divs = getdivs(N//2) # For factor()
# Solve diophantine equation p^2+r^2+p*r=y^2 <=> (2r+p)^2-y^2=-3*p^2
for p in range(1, N//2):
for u in gendivs(divs, p):
v = -3*p*p//u
if (u-v)&3 or u+v<4*p: continue
r = (u+v-2*p)//4
if r<N:
P[p].add(r)
ok.add((p,r))
for p in P:
if len(P[p]) < 2: continue
for q,r in combinations(sorted(P[p]), 2):
if (q,r) in ok:
from primes import getdivs, factsum
N = 10 ** 6
divs = getdivs(N)
visited = set()
best = (0, 0)
for n in range(2, N + 1):
(i, p, chain) = (n, {}, [])
while i > 1 and i <= N and i not in visited:
visited.add(i)
p[i] = len(chain)
chain.append(i)
i = factsum(divs, i) - i # next
if i in p:
best = max(best, (len(chain) - p[i], min(chain[p[i] :])))
print(best)