55 lines
1.2 KiB
Python
55 lines
1.2 KiB
Python
|
#!/usr/bin/env python3
|
||
|
|
|
||
|
|
from lib import primegen
|
||
|
|
from math import log
|
||
|
|
from operator import mul
|
||
|
|
from functools import reduce
|
||
|
|
|
||
|
|
def calc(pows):
|
||
|
|
return (reduce(mul, (2*p + 1 for p in pows)) + 1) // 2
|
||
|
|
|
||
|
|
def increment(i, pows):
|
||
|
|
n = 0
|
||
|
|
if i < len(pows):
|
||
|
|
n = pows[i]
|
||
|
|
return [n + 1] * (i+1) + pows[i+1:]
|
||
|
|
|
||
|
|
def val(pows):
|
||
|
|
return sum(p*v for p, v in zip(pows, vals))
|
||
|
|
|
||
|
|
def fpwof2(pows, n):
|
||
|
|
if len(pows) == 1:
|
||
|
|
return n-1
|
||
|
|
r = (2*n - 1) // reduce(mul, (2*p + 1 for p in pows[1:]))
|
||
|
|
r = (r - 1) // 2
|
||
|
|
while calc([r] + pows[1:]) < n:
|
||
|
|
r += 1
|
||
|
|
return r
|
||
|
|
|
||
|
|
N = 4 * 10**6
|
||
|
|
|
||
|
|
primes = list(primegen(100))
|
||
|
|
vals = [log(p) / log(2) for p in primes]
|
||
|
|
|
||
|
|
i = 0
|
||
|
|
pows = [0]
|
||
|
|
best = fpwof2(pows, N)
|
||
|
|
best_pows = None
|
||
|
|
|
||
|
|
while not (val(pows) >= best and sum(pows) == len(pows)):
|
||
|
|
if not i:
|
||
|
|
pows[0] = fpwof2(pows, N)
|
||
|
|
if len(pows) > 1 and pows[0] < pows[1]:
|
||
|
|
pows[0] = pows[1]
|
||
|
|
if val(pows) < best:
|
||
|
|
best = val(pows)
|
||
|
|
best_pows = pows
|
||
|
|
i = 1
|
||
|
|
pows = increment(i, pows)
|
||
|
|
if val(pows) >= best:
|
||
|
|
i += 1
|
||
|
|
else:
|
||
|
|
i = 0
|
||
|
|
|
||
|
|
print(reduce(mul, (n**pw for n, pw in zip(primes, best_pows))))
|