Zumkeller numbers: Difference between revisions
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m →{{header|Pascal}}: added "big" non-zumkeller numbers like 10884600 with 72 divisors |
→{{header|Pascal}}: checked all odd Zumkeller up to 5E8,distribution of count of divisors |
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Real time: 0.659 s CPU share: 99.05 % |
Real time: 0.659 s CPU share: 99.05 % |
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</pre> |
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Tested odd zumkeller numbers up to 500,000,000 aka 5*10^8 , which takes 14h <BR> |
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'''All 205283 odd abundant numbers less than 10^8 that have even abundance are Zumkeller numbers. - T. D. Noe, Nov 14 2010'''<BR> |
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And yes there was no odd zumkeller with odd abundance->last prime factor must have a even power >0 2,4,6... |
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<pre> 1 h5m33 ->138978315 runtime 3933.063 s |
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+12 h ->482567085 |
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+13 h ->501864363 stopped |
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count;number;SumOfDivs;CountofDivs;number : prime decomposition |
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10159 4999995; 12257280; 128 ; 4999995 : 3^3*5*7*11*13*37 |
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10160 5000625; 10396672; 60 ; 5000625 : 3^2*5^4*7*127 |
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20637 9999825; 20570112; 96 ; 9999825 : 3*5^2*11*17*23*31 |
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20638 10000305; 20217600; 48 ; 10000305 : 3^2*5*7*53*599 |
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41463 19999875; 40135680; 64 ; 19999875 : 3*5^3*7*19*401 |
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41464 20000925; 45372096; 120 ; 20000925 : 3^4*5^2*7*17*83 |
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62002 29999475; 66852864; 144 ; 29999475 : 3^2*5^2*11*17*23*31 |
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62003 30000915; 62208000; 64 ; 30000915 : 3^3*5*7*53*599 |
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82513 39999645; 82697472; 48 ; 39999645 : 3^2*5*7*23*5521 |
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82514 40000275; 82985760; 72 ; 40000275 : 3^2*5^2*7*109*233 |
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103001 49999635; 104884416; 48 ; 49999635 : 3^2*5*7*17*9337 |
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103002 50000895; 102735360; 48 ; 50000895 : 3^5*5*7*5879 |
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205283 99999375; 200935680; 80 ; 99999375 : 3*5^4*7*19*401 //205283 odd abundant numbers less than 10^8 |
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205284 100000845; 217728000; 128 ; 100000845 : 3^3*5*7*29*41*89 |
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307454 149999535; 307841040; 72 ; 149999535 : 3^2*5*7^2*59*1153 |
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307455 150000165; 306748416; 48 ; 150000165 : 3^2*5*7*31*15361 |
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409569 199999305; 400443264; 48 ; 199999305 : 3^2*5*11*17*23767 |
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409570 200000115; 403269984; 36 ; 200000115 : 3^2*5*7^2*90703 |
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511807 249999435; 521314560; 48 ; 249999435 : 3^2*5*7*19*41771 |
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511808 250000065; 506782848; 48 ; 250000065 : 3^2*5*7*43*18457 |
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613721 299998755; 609523200; 32 ; 299998755 : 3^3*5*7*317459 |
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613722 300000645; 611696640; 64 ; 300000645 : 3^3*5*7*523*607 |
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715573 349998705; 742072320; 64 ; 349998705 : 3^3*5*7*23*16103 |
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715574 350000595; 717044064; 40 ; 350000595 : 3^4*5*7*123457 |
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817456 399998865; 808206336; 64 ; 399998865 : 3*5*7*17*23*9743 |
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817457 400000293; 803312640; 96 ; 400000293 : 3^2*7*11*17*19*1787 |
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919451 449999235; 922184640; 48 ; 449999235 : 3^2*5*7*29*49261 |
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919452 450000495; 943841280; 64 ; 450000495 : 3^3*5*7*31*15361 |
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1021438 499999185; 1052101440; 72 ; 499999185 : 3^2*5*7^2*23*9859 |
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1021439 500000445; 1027178880; 48 ; 500000445 : 3^5*5*7*58789 |
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ODD Zumkeller Index;CoD Count of Divisors;Average CoD;Zumkeller number |
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1; 16; 16.0000;945 : 3^3*5*7 |
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2; 18; 18.0000;1575 : 3^2*5^2*7 |
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4; 20; 19.0000;2835 : 3^4*5*7 |
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5; 24; 24.0000;3465 : 3^2*5*7*11 |
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24; 32; 24.4211;10395 : 3^3*5*7*11 |
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36; 36; 27.5000;17325 : 3^2*5^2*7*11 |
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69; 40; 30.4242;31185 : 3^4*5*7*11 |
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101; 48; 33.3125;45045 : 3^2*5*7*11*13 |
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246; 54; 37.7931;121275 : 3^2*5^2*7^2*11 |
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272; 64; 41.1538;135135 : 3^3*5*7*11*13 |
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439; 72; 43.2335;225225 : 3^2*5^2*7*11*13 |
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814; 80; 45.8027;405405 : 3^4*5*7*11*13 |
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1366; 96; 49.0688;675675 : 3^3*5^2*7*11*13 |
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3126; 108; 53.1364;1576575 : 3^2*5^2*7^2*11*13 |
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4025; 120; 55.8843;2027025 : 3^4*5^2*7*11*13 |
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4573; 128; 56.6752;2297295 : 3^3*5*7*11*13*17 |
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7715; 144; 58.4978;3828825 : 3^2*5^2*7*11*13*17 |
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14116; 160; 61.1239;6891885 : 3^4*5*7*11*13*17 |
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23733; 192; 63.7696;11486475 : 3^3*5^2*7*11*13*17 |
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55414; 216; 67.8331;26801775 : 3^2*5^2*7^2*11*13*17 |
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71154; 240; 70.7454;34459425 : 3^4*5^2*7*11*13*17 |
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89984; 256; 72.0990;43648605 : 3^3*5*7*11*13*17*19 |
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149543; 288; 74.2782;72747675 : 3^2*5^2*7*11*13*17*19 |
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268601; 320; 77.3901;130945815 : 3^4*5*7*11*13*17*19 |
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446838; 384; 80.4003;218243025 : 3^3*5^2*7*11*13*17*19 |
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last 501864363 |
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1025232 84.3602; |
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1025232 80.7680;501864363 : 3^3*7*11*13*31*599 |
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CntOfDivs|Count | last occurence |
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16 1 945 |
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18 2 2205 |
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20 1 2835 |
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24 37 32445 |
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28 1 25515 |
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30 5 108045 |
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32 44011 501862095 |
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36 47777 501859575 |
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40 16114 501848865 |
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42 6 5294205 |
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44 1 2066715 |
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48 197324 501856425 |
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50 4 972405 |
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52 1 18600435 |
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54 2795 499226175 |
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56 2254 501650415 |
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60 11478 501809175 |
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64 154291 501863985 |
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66 4 19190925 |
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70 8 47647845 |
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72 102440 501846975 |
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78 4 172718325 |
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80 34227 501843195 |
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84 1892 501788925 |
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88 71 498078315 |
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90 1987 501185475 |
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96 211623 501863175 |
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98 4 428830605 |
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100 670 500833125 |
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104 8 496897335 |
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108 13834 501858225 |
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110 3 479773125 |
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112 4445 501803505 |
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120 20477 501833475 |
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126 310 501701445 |
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128 67263 501864363 |
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132 32 485678025 |
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140 138 500731875 |
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144 48901 501862725 |
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150 136 500788575 |
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160 11220 501808125 |
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162 454 501511725 |
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168 1299 501570225 |
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176 4 456744015 |
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180 1599 501780825 |
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192 19903 501838155 |
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200 173 501744375 |
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210 6 481340475 |
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216 2097 501752475 |
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224 274 501854535 |
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240 1368 501860205 |
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252 42 499200975 |
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256 1163 501756255 |
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270 21 495685575 |
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280 1 456080625 |
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288 871 501666165 |
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300 2 463876875 |
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320 92 499926735 |
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324 9 471395925 |
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336 6 485269785 |
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360 13 500675175 |
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384 32 498513015 |
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</pre> |
</pre> |
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