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weird numbers
A number which is abundant but not pseudoperfect. more

The first 600 weird numbers :
70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990, 18410, 18830, 18970, 19390, 19670, 19810, 20510, 21490, 21770, 21910, 22190, 23170, 23590, 24290, 24430, 24710, 25130, 25690, 26110, 26530, 26810, 27230, 27790, 28070, 28630, 29330, 29470, 30170, 30310, 30730, 31010, 31430, 31990, 32270, 32410, 32690, 33530, 34090, 34370, 34930, 35210, 35630, 36470, 36610, 37870, 38290, 38990, 39410, 39830, 39970, 40390, 41090, 41510, 41930, 42070, 42490, 42910, 43190, 43330, 44170, 44870, 45010, 45290, 45356, 45710, 46130, 46270, 47110, 47390, 47810, 48370, 49070, 49630, 50330, 50890, 51310, 51730, 52010, 52570, 52990, 53270, 53830, 54110, 55090, 55790, 56630, 56770, 57470, 57610, 57890, 58030, 58730, 59710, 59990, 60130, 60410, 61390, 61670, 61810, 62090, 63490, 63770, 64330, 65030, 65590, 65870, 66290, 66710, 67690, 67970, 68390, 68810, 69370, 69790, 70630, 70910, 71330, 71470, 72170, 72310, 72730, 73430, 73570, 73616, 74270, 74410, 74830, 76090, 76370, 76510, 76790, 77210, 77630, 78190, 78610, 79030, 80570, 80710, 81410, 81970, 82670, 83090, 83312, 83510, 84070, 84910, 85190, 85610, 86030, 86170, 86590, 87430, 88130, 89390, 89530, 89810, 90230, 90370, 90790, 91070, 91210, 91388, 91490, 92330, 92470, 92890, 95270, 95690, 96110, 96670, 97930, 98630, 99610, 99890, 100030, 100310, 100730, 101290, 101570, 101710, 102130, 102970, 103670, 103810, 104090, 104230, 104510, 104930, 105770, 106610, 107170, 108010, 108430, 108710, 109130, 109690, 109970, 110530, 110810, 111790, 112070, 112490, 112630, 112910, 113072, 113330, 113470, 113890, 114590, 115990, 116410, 116690, 116830, 118510, 118790, 118930, 119630, 120470, 120610, 121310, 121870, 122290, 122710, 123130, 124390, 124810, 125090, 125230, 126070, 126770, 127610, 128170, 129290, 130270, 130690, 130970, 131110, 131390, 131530, 132230, 133070, 133490, 133910, 135170, 135310, 136430, 136570, 138110, 138530, 139090, 139510, 139790, 139930, 140210, 140770, 141190, 141890, 142030, 142730, 143710, 144410, 144830, 145670, 145810, 146090, 146230, 146930, 147770, 147910, 149030, 149170, 149590, 149870, 150010, 150710, 151270, 152530, 154210, 154490, 154910, 155470, 156590, 156730, 157010, 157570, 158690, 158830, 159110, 159670, 160090, 160510, 160790, 161630, 161770, 163310, 163730, 163870, 164290, 164570, 164990, 165970, 166390, 166670, 166810, 167230, 167510, 167930, 168770, 169190, 169610, 170590, 170870, 171290, 172130, 172690, 173110, 173390, 175210, 176470, 177170, 177730, 178010, 178430, 178570, 178990, 180530, 181370, 181510, 182630, 183190, 183470, 184310, 185290, 185990, 186130, 186410, 186970, 187390, 187810, 188090, 188230, 188510, 188930, 189490, 189770, 189910, 190330, 191030, 191170, 191870, 192430, 192710, 193690, 194390, 195230, 195370, 195790, 196070, 196210, 197330, 198310, 198590, 199010, 199570, 199990, 200270, 201530, 202090, 202790, 203210, 203630, 204190, 204890, 205730, 206710, 206990, 207410, 207830, 207970, 209930, 210070, 210770, 211330, 211610, 212590, 212870, 213430, 214270, 214690, 215530, 215810, 216230, 217630, 218330, 218470, 219590, 221410, 221690, 221830, 222670, 222952, 223090, 223370, 224210, 224630, 225190, 225470, 226030, 227570, 227710, 227990, 228130, 228970, 230930, 231070, 231490, 231910, 232330, 232610, 233030, 233170, 234010, 234290, 235130, 235270, 235970, 236110, 237230, 237370, 238490, 238910, 240310, 241430, 241990, 242270, 242410, 242690, 242830, 243892, 244370, 244930, 245770, 246190, 246890, 247030, 247310, 247730, 247870, 248290, 248990, 249130, 249970, 250670, 250810, 251510, 252490, 252910, 253190, 253610, 254012, 254170, 254590, 255010, 256130, 256970, 257110, 257390, 258370, 258790, 259070, 259630, 260330, 260890, 261310, 261730, 263270, 263690, 263830, 264530, 265510, 265790, 266210, 267470, 267610, 268310, 269290, 269570, 269710, 270410, 271390, 271670, 272230, 273490, 273770, 274190, 274330, 274610, 275030, 275170, 276010, 276290, 277690, 279230, 280070, 280210, 280490, 280910, 281330, 281470, 281890, 283430, 283570, 283990, 285110, 285530, 286370, 286510, 286930, 287770, 288890, 289030, 289310, 289730, 290710, 290990, 291130, 292390, 294070, 294770, 295190, 295330, 296030, 296170, 296870, 297010, 297710, 298130, 298270, 298970, 299110, 299810, 300230, 300790, 302890, 303590, 303730, 304430, 304990, 305410, 306110, 307370, 307790, 308630, 309470, 309610, 310870, 311290, 311570, 311990, 312410, 313670, 313810, 314510, 315490, 315910, 316190, 316330, 316610, 318290, 318430.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 7784 values, from 70 to 4999330).

n\r 0  1 
277840 2 
3038913893 3 
4718070660 4 
57066180189180169 5 
6003893038910 6 
77063119124125118121114 7 
827035330691035330 8 
9013051298013041300012821295 9 
10706601890169018001800 10 
11689707706708708713713716712707705

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.