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Jordan-Polya numbers
A number  $n$  is a Jordan-Polya number if it can be written as the product of factorial numbers.

For example,  $92160$  is a Jordan-Polya number, because it can be written as  $(2!)^7\cdot 6!$.

Jordan-Polya numbers arise in the following simple combinatorial problem. If  $k$  groups of  $n_1,n_2,\dots,n_k$  distinct objects are given, then the number of distinct permutations of the  $n_1+n_2+\cdots+n_k$  objects which maintain objects of the same group adjacent are  $k!\cdot n_1!\cdot n_2!\cdots n_k!$, a Jordan-Polya number.

The first Jordan-Polya numbers are 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 more terms

Jordan-Polya numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 24 32 + 9784472371200 9906778275840 aban 12 16 + 864 960 abundant 12 24 + 47775744 49766400 Achilles 72 288 + 49533891379200 49941577728000 admirable 12 24 120 30240 alternating 12 16 + 41472 147456 amenable 12 16 + 990904320 995328000 apocalyptic 192 384 + 27648 28800 arithmetic 96 432 + 9676800 9953280 astonishing 216 betrothed 48 binomial 36 120 c.pentagonal 16 c.triangular 64 cake 64 576 2048 compositorial 24 192 + 5267275776000 115880067072000 congruent 24 96 + 8847360 9953280 constructible 12 16 + 562949953421312 844424930131968 cube 64 216 + 812479653347328 949978046398464 Cunningham 24 48 + 5040 25920 d-powerful 24 2048 + 345600 7864320 deficient 16 32 + 4194304 8388608 dig.balanced 12 120 + 7741440 8847360 double fact. 48 384 + 1961990553600 51011754393600 droll 72 240 + 722204136308736 847579919155200 Duffinian 16 32 + 8388608 9437184 eban 32 36 64 economical 16 32 + 19353600 19906560 enlightened 256 2048 + 231928233984 274877906944 equidigital 16 32 + 14515200 19353600 eRAP 24 esthetic 12 32 432 3456 Eulerian 120 evil 12 24 + 990904320 995328000 factorial 24 120 + 20922789888000 355687428096000 Fibonacci 144 Friedman 128 216 + 983040 995328 frugal 128 256 + 990904320 995328000 gapful 120 192 + 99532800000 99632332800 happy 32 192 + 8957952 9437184 harmonic 30240 Harshad 12 24 + 9909043200 9953280000 hexagonal 120 highly composite 12 24 + 10080 20160 house 32 hungry 144 iban 12 24 + 311040 414720 idoneal 12 16 + 120 240 impolite 16 32 + 281474976710656 562949953421312 inconsummate 216 432 + 725760 829440 interprime 12 64 + 72576000 74649600 junction 216 1024 + 79626240 94371840 katadrome 32 64 + 4320 8640 Leyland 32 512 + 33554432 17832200896512 lonely 120 Lynch-Bell 12 24 + 13824 18432 magnanimous 12 16 32 512 metadrome 12 16 + 256 3456 nialpdrome 32 64 + 8640 86400 nonagonal 24 nude 12 24 + 226492416 429981696 O'Halloran 12 36 oban 12 16 + 768 960 octagonal 96 8640 odious 16 32 + 928972800 967458816 pancake 16 4096 panconsummate 12 24 + 72 144 pandigital 120 216 30720 pentagonal 12 pernicious 12 24 + 9437184 9676800 Perrin 12 plaindrome 12 16 + 3456 12288 power 16 32 + 45137758519296 47775744000000 powerful 16 32 + 990677827584000 995515121664000 practical 12 16 + 9676800 9953280 prim.abundant 12 pronic 12 72 240 pseudoperfect 12 24 + 983040 995328 Ruth-Aaron 16 24 Saint-Exupery 480 3840 + 890604418498560 974098582732800 self 64 288 + 644972544 905969664 Smith 576 7077888 8957952 square 16 36 + 958878292377600 989560464998400 straight-line 432 864 3456 strobogrammatic 96 super Niven 12 24 + 80640 604800 super-d 13824 16384 + 4718592 4838400 superabundant 12 24 + 5040 10080 tau 12 24 + 990904320 995328000 tetrahedral 120 triangular 36 120 tribonacci 24 trimorphic 24 uban 12 16 + 72 96 Ulam 16 36 + 7077888 8294400 unprimeable 512 1920 + 8388608 8847360 untouchable 96 120 + 933120 967680 upside-down 64 8192 vampire 186624 wasteful 12 24 + 4838400 9676800 Zuckerman 12 24 + 161243136 429981696 Zumkeller 12 24 + 92160 98304