Jordan-Pólya numbers: Difference between revisions

=={{header|Python}}==

{{trans|Java}}

<syntaxhighlight lang="Python">

from collections import defaultdict

from itertools import product

class JordanPolyaNumbers:

def __init__(self):

self.jordan_polya_set = set()

self.decompositions = defaultdict(dict)

def create_jordan_polya(self):

self.jordan_polya_set.add(1)

next_set = set()

self.decompositions[1] = {}

factorial = 1

for multiplier in range(2, 21):

factorial *= multiplier

for number in list(self.jordan_polya_set):

while number <= 2**63 - 1 // factorial:

original = number

number *= factorial

next_set.add(number)

self.decompositions[number] = self.decompositions[original].copy()

self.decompositions[number][multiplier] = self.decompositions[number].get(multiplier, 0) + 1

self.jordan_polya_set.update(next_set)

next_set.clear()

def to_string(self, a_map):

result = ""

for key in sorted(a_map.keys(), reverse=True):

exponent = a_map[key]

result += f"{key}!" + ("" if exponent == 1 else f"^{exponent}") + " * "

return result[:-3]

def display_results(self):

below_hundred_million = max(n for n in self.jordan_polya_set if n < 100_000_000)

jordan_polya = sorted(list(self.jordan_polya_set))

print("The first 50 Jordan-Polya numbers:")

for i in range(50):

end = "\n" if (i % 10 == 9) else ""

print(f"{jordan_polya[i]:5}", end=end)

print()

print(f"The largest Jordan-Polya number less than 100 million: {below_hundred_million}")

print()

for i in [800, 1050, 1800, 2800, 3800]:

print(f"The {i}th Jordan-Polya number is: {jordan_polya[i-1]}"

f" = {self.to_string(self.decompositions[jordan_polya[i-1]])}")

if __name__ == "__main__":

jpn = JordanPolyaNumbers()

jpn.create_jordan_polya()

jpn.display_results()

</syntaxhighlight>

{{out}}

<pre>

The first 50 Jordan-Polya numbers:

1 2 4 6 8 12 16 24 32 36

48 64 72 96 120 128 144 192 216 240

256 288 384 432 480 512 576 720 768 864

960 1024 1152 1296 1440 1536 1728 1920 2048 2304

2592 2880 3072 3456 3840 4096 4320 4608 5040 5184

The largest Jordan-Polya number less than 100 million: 99532800

The 800th Jordan-Polya number is: 18345885696 = 4!^7 * 2!^2

The 1050th Jordan-Polya number is: 139345920000 = 8! * 5!^3 * 2!

The 1800th Jordan-Polya number is: 9784472371200 = 6!^2 * 4!^2 * 2!^15

The 2800th Jordan-Polya number is: 439378587648000 = 14! * 7!

The 3800th Jordan-Polya number is: 7213895789838336 = 4!^8 * 2!^16

</pre>