Talk:Jordan-Pólya numbers: Difference between revisions

The 1050th jp number is 139,345,920,000. One and I suspect the only possible factorisation is 7! * 5!^3 * 2!^4, but the Phix/Julia/Wren entries are not getting that. I have thought of a better strategy, based on the prime powers, but it is not straightforward and would naturally produce the ''lowest'' factorials - I ''think'' I might have just thought of a way to convert that to the highest factorials... In the meantime, some examples:

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92,160 = 6! * 2!^7, or

92,160 = 5! * 3! * 2!^7

18,345,885,696 = 4!^7 * 2!^2, or

18,345,885,696 = 3!^7 * 2!^16

139,345,920,000 = 7! * 5!^3 * 2!^4 (only one?)

18,345,885,696 = 4!^7 * 2!^2, or

18,345,885,696 = 3!^7 * 2!^16

724,775,731,200 = 6! * 5! * 2!^23, or

724,775,731,200 = 5!^2 * 3! * 2!^23

9,784,472,371,200 = 6!^2 * 4!^2 * 2!^15, or

9,784,472,371,200 = 5!^2 * 3!^4 * 2!^19

439,378,587,648,000 = 14! * 7! (only one?)

7,213,895,789,838,336 = 4!^8 * 2!^16, or

7,213,895,789,838,336 = 3!^8 * 2!^32

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There are probably only a few ways to do each, maybe show them all? --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 23:52, 9 June 2023 (UTC)