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#!/usr/local/bin/python3
#
# See https://theweeklychallenge.org/blog/perl-weekly-challenge-148
#
#
# Run as: python ch-2.py
#
import math
COUNT = 5
A = 0
B = 1
C = 2
SUM = 3
out = []
for i in range (COUNT):
out . append ([999999, 999999, 999999, 999999 * 3])
max_index = 0
k = 0
while 3 * k + 2 < out [max_index] [SUM]:
a = 3 * k + 2
f1 = k + 1
f2 = 8 * k + 5
d1 = []
for i in range (1, f1 + 1):
if i * i > f1:
break
if f1 % i == 0:
d1 . append (i)
if i != f1 // i:
d1 . append (f1 // i)
d2 = []
for i in range (1, f2 + 1):
if i * i > f2:
break
if f2 % i == 0:
s1 = math . isqrt (i)
s2 = math . isqrt (f2 // i)
if s1 * s1 == i:
d2 . append (s1)
if s2 * s2 == f2 // i and s1 != s2:
d2 . append (s2)
for d1v in d1:
for d2v in d2:
b = d1v * d2v
c = f1 * f1 * f2 // (b * b)
if a + b + c < out [max_index] [SUM]:
seen = False
for i in range (COUNT):
if out [i] [A] == a and out [i] [B] == b:
seen = true
break
if seen:
break
out [max_index] = [a, b, c, a + b + c]
max_index = 0
max_sum = out [max_index] [SUM]
for i in range (1, COUNT):
if max_sum < out [i] [SUM]:
max_sum = out [i] [SUM]
max_index = i
k = k + 1
for i in range (COUNT):
print (out [i] [A], out [i] [B], out [i] [C])
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