Search a number
Jordan-Polya numbers
A number which can be written as a product of factorials. more

The first 600 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, 5760, 6144, 6912, 7680, 7776, 8192, 8640, 9216, 10080, 10368, 11520, 12288, 13824, 14400, 15360, 15552, 16384, 17280, 18432, 20160, 20736, 23040, 24576, 25920, 27648, 28800, 30240, 30720, 31104, 32768, 34560, 36864, 40320, 41472, 46080, 46656, 49152, 51840, 55296, 57600, 60480, 61440, 62208, 65536, 69120, 73728, 80640, 82944, 86400, 92160, 93312, 98304, 103680, 110592, 115200, 120960, 122880, 124416, 131072, 138240, 147456, 155520, 161280, 165888, 172800, 181440, 184320, 186624, 196608, 207360, 221184, 230400, 241920, 245760, 248832, 262144, 276480, 279936, 294912, 311040, 322560, 331776, 345600, 362880, 368640, 373248, 393216, 414720, 442368, 460800, 483840, 491520, 497664, 518400, 524288, 552960, 559872, 589824, 604800, 622080, 645120, 663552, 691200, 725760, 737280, 746496, 786432, 829440, 884736, 921600, 933120, 967680, 983040, 995328, 1036800, 1048576, 1088640, 1105920, 1119744, 1179648, 1209600, 1244160, 1290240, 1327104, 1382400, 1451520, 1474560, 1492992, 1572864, 1658880, 1679616, 1728000, 1769472, 1843200, 1866240, 1935360, 1966080, 1990656, 2073600, 2097152, 2177280, 2211840, 2239488, 2359296, 2419200, 2488320, 2580480, 2654208, 2764800, 2903040, 2949120, 2985984, 3110400, 3145728, 3317760, 3359232, 3456000, 3538944, 3628800, 3686400, 3732480, 3870720, 3932160, 3981312, 4147200, 4194304, 4354560, 4423680, 4478976, 4718592, 4838400, 4976640, 5160960, 5308416, 5529600, 5598720, 5806080, 5898240, 5971968, 6220800, 6291456, 6531840, 6635520, 6718464, 6912000, 7077888, 7257600, 7372800, 7464960, 7741440, 7864320, 7962624, 8294400, 8388608, 8709120, 8847360, 8957952, 9437184, 9676800, 9953280, 10077696, 10321920, 10368000, 10616832, 11059200, 11197440, 11612160, 11796480, 11943936, 12441600, 12582912, 13063680, 13271040, 13436928, 13824000, 14155776, 14515200, 14745600, 14929920, 15482880, 15728640, 15925248, 16588800, 16777216, 17418240, 17694720, 17915904, 18662400, 18874368, 19353600, 19906560, 20155392, 20643840, 20736000, 21233664, 21772800, 22118400, 22394880, 23224320, 23592960, 23887872, 24883200, 25165824, 25401600, 26127360, 26542080, 26873856, 27648000, 28311552, 29030400, 29491200, 29859840, 30965760, 31457280, 31850496, 33177600, 33554432, 33592320, 34836480, 35389440, 35831808, 37324800, 37748736, 38707200, 39191040, 39813120, 39916800, 40310784, 41287680, 41472000, 42467328, 43545600, 44236800, 44789760, 46448640, 47185920, 47775744, 49766400, 50331648, 50803200, 52254720, 53084160, 53747712, 55296000, 56623104, 58060800, 58982400, 59719680, 60466176, 61931520, 62208000, 62914560, 63700992, 66355200, 67108864, 67184640, 69672960, 70778880, 71663616, 72576000, 74649600, 75497472, 77414400, 78382080, 79626240, 79833600, 80621568, 82575360, 82944000, 84934656, 87091200, 88473600, 89579520, 92897280, 94371840, 95551488, 99532800, 100663296, 101606400, 104509440, 106168320, 107495424, 110592000, 111974400, 113246208, 116121600, 117964800, 119439360, 120932352, 123863040, 124416000, 125829120, 127401984, 130636800, 132710400, 134217728, 134369280, 139345920, 141557760, 143327232, 145152000, 149299200, 150994944, 152409600, 154828800, 156764160, 159252480, 159667200, 161243136, 165150720, 165888000, 169869312, 174182400, 176947200, 179159040, 185794560, 188743680, 191102976, 199065600, 201326592, 201553920, 203212800, 207360000, 209018880, 212336640, 214990848, 221184000, 223948800, 226492416, 232243200, 235146240, 235929600, 238878720, 239500800, 241864704, 247726080, 248832000, 251658240, 254803968, 261273600, 265420800, 268435456, 268738560, 278691840, 283115520, 286654464, 290304000, 298598400, 301989888, 304819200, 309657600, 313528320, 318504960, 319334400, 322486272, 330301440, 331776000, 339738624, 348364800, 353894400, 358318080, 362797056, 371589120, 373248000, 377487360, 382205952, 398131200, 402653184, 403107840, 406425600, 414720000, 418037760, 424673280, 429981696, 435456000, 442368000, 447897600, 452984832, 464486400, 470292480, 471859200, 477757440, 479001600, 483729408, 495452160, 497664000, 503316480, 509607936, 522547200, 530841600, 536870912, 537477120, 557383680, 566231040, 573308928, 580608000, 597196800, 603979776, 609638400, 619315200, 627056640, 637009920, 638668800, 644972544, 660602880, 663552000, 671846400, 679477248, 696729600, 707788800, 716636160, 725594112, 743178240, 746496000, 754974720, 764411904, 783820800, 796262400, 805306368, 806215680, 812851200, 829440000, 836075520, 849346560, 859963392, 870912000, 884736000, 895795200, 905969664, 914457600, 928972800, 940584960, 943718400, 955514880, 958003200, 967458816, 990904320, 995328000, 1006632960, 1019215872, 1045094400, 1061683200, 1073741824, 1074954240, 1114767360, 1132462080, 1146617856, 1161216000, 1194393600, 1207959552, 1209323520, 1219276800, 1238630400, 1244160000, 1254113280, 1274019840, 1277337600, 1289945088, 1321205760, 1327104000, 1343692800, 1358954496, 1393459200, 1410877440, 1415577600, 1433272320, 1437004800, 1451188224, 1486356480, 1492992000, 1509949440, 1528823808, 1567641600, 1592524800, 1610612736, 1612431360, 1625702400, 1658880000, 1672151040, 1698693120, 1719926784, 1741824000, 1769472000, 1791590400, 1811939328, 1828915200, 1857945600, 1881169920, 1887436800, 1911029760, 1916006400, 1934917632, 1981808640, 1990656000, 2013265920, 2038431744, 2090188800, 2123366400, 2147483648, 2149908480, 2176782336, 2229534720, 2239488000, 2264924160, 2293235712, 2322432000, 2388787200, 2415919104, 2418647040, 2438553600.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 3065 values, from 1 to 995515121664000).

n\r 0  1 
230641 2 
330152525 3 
43062120 4 
52550136131122126 5 
630151250240 6 
71513291277229262240253 7 
830591103010 8 
929249946884588 9 
10255011310126013501220 10 
11473261261258261259258258258259259

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.