Talk:Zumkeller numbers: Difference between revisions
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== Where to find count of Zumkeller to verify solutions.Is there a constant ratio 0.228...? == |
== Where to find count of Zumkeller to verify solutions.Is there a constant ratio 0.228...? == |
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I have modified the program to run up to 1E9 |
I have modified the program to run up to 1E9.On AMD 2200G Linux 64-bit |
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<pre> |
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<pre>Count of Zumkeller numbers up to 1,000,000,000 |
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Start 1 at 1 |
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count n |
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100000000 tested found 22879037 ratio 0.2287904 recursion 1.101 runtime 9.777 s |
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224 1000 time 0.004 s |
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200000000 tested found 45744040 ratio 0.2287202 recursion 1.116 runtime 10.640 s |
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2294 10000 time 0.005 s |
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300000000 tested found 68603020 ratio 0.2286767 recursion 1.171 runtime 11.159 s |
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23051 100000 time 0.016 s |
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400000000 tested found 91458844 ratio 0.2286471 recursion 1.230 runtime 11.506 s |
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229026 1000000 time 0.241 s |
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500000000 tested found 114316149 ratio 0.2286323 recursion 1.283 runtime 11.770 s |
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2287889 10000000 time 5.031 s |
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600000000 tested found 137176153 ratio 0.2286269 recursion 1.332 runtime 20.701 s |
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22879037 100000000 time 114.117 s |
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700000000 tested found 160037821 ratio 0.2286255 recursion 2.834 runtime 22.288 s |
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228620758 1000000000 time 2763.437 s |
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800000000 tested found 182899550 ratio 0.2286244 recursion 2.786 runtime 13.064 s |
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900000000 tested found 205760422 ratio 0.2286227 recursion 2.691 runtime 12.682 s |
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count of count of last with |
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1000000000 tested found 228620760 ratio 0.2286208 recursion 2.620 runtime 12.842 s |
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divisors occurence this count |
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total 136s = 2m16s ( 228620758 1000000000 time 2763.437 s (2 with high recursion >1e8 added as true ) ) |
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</pre> |
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6 3 28 |
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[[user Horst.h|Horst.h]] 06:28, 20 June 2021 (UTC) |
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8 9327007 999999894 |
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10 10 496 |
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12 10043024 999999996 |
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14 30 8128 |
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16 29081897 999999978 |
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18 3061 999625548 |
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20 4470960 999999952 |
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22 308 2087936 |
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24 28328093 999999948 |
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26 1027 33550336 |
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28 1640168 999999680 |
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30 22909 999449264 |
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32 34193954 999999912 |
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34 1778 998834176 |
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36 5108860 999999740 |
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38 528 996933632 |
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40 8732428 999999984 |
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42 39946 999995456 |
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44 165649 999992320 |
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46 50 977272832 |
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48 30404269 999999980 |
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50 7343 999930064 |
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52 43316 999993344 |
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54 127846 999986004 |
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56 2231014 999999918 |
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58 1 805306368 |
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60 2285988 999999056 |
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64 17785246 999999966 |
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66 14418 999857152 |
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68 2944 999620608 |
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70 10065 999863488 |
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72 7612581 999999612 |
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76 751 999030784 |
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78 6291 999657472 |
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80 5097772 999999888 |
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84 550440 999998400 |
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88 125242 999994368 |
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90 99455 999990864 |
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92 45 994050048 |
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96 12888461 999999968 |
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98 2609 999978048 |
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100 137019 1000000000 |
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102 546 998703104 |
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104 29385 999985152 |
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108 672289 999999900 |
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110 1977 999392256 |
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112 983872 999999168 |
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114 163 993263616 |
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120 1793678 999999756 |
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126 30520 999949248 |
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128 4026453 999999750 |
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130 565 998977536 |
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132 32547 999982080 |
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136 1471 999882752 |
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138 10 868220928 |
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140 48252 999998784 |
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144 3107948 999999744 |
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150 13569 999970000 |
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152 301 999555072 |
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154 287 993912768 |
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156 7989 999788544 |
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160 1348234 999998480 |
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162 23768 999878400 |
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168 327063 999999936 |
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170 49 960823296 |
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176 41522 999945216 |
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180 191844 999997200 |
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182 77 988360704 |
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184 6 968884224 |
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190 14 997982208 |
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192 2404911 999999990 |
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196 3408 999884736 |
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198 2285 999756800 |
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200 74414 999987120 |
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204 434 997392384 |
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208 8206 999837696 |
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210 5189 999720000 |
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216 338514 999996900 |
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220 2270 999889920 |
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224 207061 999994560 |
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228 85 979107840 |
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234 622 998502400 |
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238 6 907739136 |
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240 503320 999999792 |
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242 4 786060288 |
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250 297 997110000 |
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252 34145 999993280 |
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256 420553 999999336 |
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260 506 999641088 |
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264 13404 999961600 |
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266 1 955514880 |
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270 7815 999967500 |
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272 236 999751680 |
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280 20719 999988416 |
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288 525917 999998880 |
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294 407 999604800 |
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300 13031 999990000 |
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304 26 994836480 |
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306 36 987955200 |
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308 213 999558144 |
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312 2573 998903808 |
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320 161781 999997680 |
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324 18434 999998208 |
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330 306 996480000 |
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336 70675 999972288 |
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340 18 992673792 |
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342 5 963379200 |
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350 137 998730000 |
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352 5606 999957504 |
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360 63310 999997488 |
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364 36 982388736 |
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378 1407 999132480 |
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380 1 743178240 |
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384 196619 999994842 |
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390 74 991678464 |
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392 1003 999000000 |
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396 1377 999429120 |
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400 13390 999979344 |
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408 49 997785600 |
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416 788 999198720 |
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420 3476 999625536 |
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432 53355 999980800 |
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440 538 998231040 |
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448 17624 999984960 |
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450 671 993322512 |
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456 1 908328960 |
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462 25 989107200 |
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468 242 998092800 |
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480 49670 999988080 |
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486 456 997210368 |
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490 11 903960000 |
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500 150 992631024 |
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504 7684 999979200 |
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510 1 928972800 |
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512 17626 999983880 |
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520 74 977080320 |
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528 1488 999060480 |
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540 3240 999791100 |
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544 3 984023040 |
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546 4 970444800 |
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550 6 995742720 |
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560 2348 999779760 |
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576 29682 999999840 |
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588 135 999044928 |
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594 49 942289920 |
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600 2171 999870480 |
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616 17 977163264 |
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624 142 999936000 |
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630 155 997012800 |
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640 6125 999989760 |
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648 2346 999532800 |
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660 65 997401600 |
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672 4038 999915840 |
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700 23 975240000 |
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702 5 858009600 |
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704 170 996602880 |
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720 4115 999702000 |
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750 8 958230000 |
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756 283 999835200 |
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768 4066 999814200 |
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780 4 987033600 |
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784 42 997738560 |
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792 84 999398400 |
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800 447 999217296 |
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810 45 968612400 |
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832 6 979292160 |
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840 236 996287040 |
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864 1338 999949860 |
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880 12 989936640 |
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882 4 987940800 |
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896 273 999311040 |
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900 63 998600400 |
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936 1 922521600 |
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960 635 999734400 |
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972 22 990662400 |
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1000 1 810810000 |
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1008 153 999028800 |
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1024 92 999999000 |
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1056 5 968647680 |
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1080 45 998917920 |
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1120 16 992431440 |
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1152 93 997682400 |
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1200 9 975466800 |
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1260 1 908107200 |
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1280 6 985944960 |
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1296 3 980179200 |
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1344 4 994593600</pre> |
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[[user Horsth|Horsth]] 06:28, 20 June 2021 (UTC) |
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== Cheating odd no 5 zumkeller numbers == |
== Cheating odd no 5 zumkeller numbers == |