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  | SPECIAL MULTIPERFECT NUMBER SEARCH |  |  |  |  |  |  |  |  |  |  
  | Numbers n for
  which sigma(n)/n = k + X with integer k and rational X |  |  |  |  |  |  |  |  |  
  | Valid in range <10.000.000
  unless otherwise noted. |  |  |  |  |  |  |  |  |  |  
  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
  | No. | sigma(n)/n | n | Registered in The OEIS database: |  |  |  |  
  | Z01 | k+1/4 | 40 (k=2) | 224 (k=2) | 360 (k=3) | 2016 (k=3) | 174592 (k=2) | 524160 (k=4) | 1571328 (k=3) |  | A218404 |  |  |  |  
  | Z02 | k+3/4 | 47616 (k=2) | 293760 (k=3) | 1782144 (k=3) | 3485664 (k=3) |  |  |  |  | A218405 |  |  |  |  
  |  |  |  |  |  |  
  | Z03 | k+1/5 | 420 (k=3) | 7440 (k=3) | 8190 (k=3) | 18600 (k=3) | 121920 (k=3) | 131040 (k=4) |  |  | A218406 |  |  |  |  
  | Z04 | k+2/5 | 30
  (k=2) | 140 (k=2) | 2480 (k=2) | 6200 (k=2) | 40640 (k=2) | 297600 (k=3) | 997920 (k=4) |  | A218407 |  |  |  |  
  | Z05 | k+3/5 | 90
  (k=2) | 3360 (k=3) | 2618880 (k=3) | 5059200 (k=3) |  |  |  |  | A218408 |  |  |  |  
  | Z06 | k+4/5 | 60
  (k=2) | 1170 (k=2) | 114660 (k=3) |  |  |  |  |  | A218427 |  |  |  |  
  |  |  |  |  |  |  
  | Z07 | k+1/6 | 18
  (k=2) | 22932 (k=3) |  |  |  |  |  |  |  |  |  |  |  
  |  | k+5/6 | - |  |  |  |  |  |  |  |  |  |  |  |  
  |  |  |  |  |  |  
  | Z08 | k+1/7 | 56
  (k=2) | 3724 (k=2) | 333312 (k=3) |  |  |  |  |  | A218428 |  |  |  |  
  | Z09 | k+2/7 | 42
  (k=2) | 3472 (k=2) | 56896 (k=2) | 2056320 (k=4) | 4021920 (k=4) | 4357080 (k=4) | 6420960 (k=4) |  | A218409 |  |  |  |  
  | Z10 | k+3/7 | 840 (k=3) | 55860 (k=3) | 1089270 (k=3) | 3666432 (k=3) | proved up to 100.000.000 | A218410 |  |  |  |  
  | Z11 | k+4/7 | 280 (k=2) | 18620 (k=2) | 411264 (k=3) | 804384 (k=3) | 871416 (k=3) | 1222144 (k=2) | 1284192 (k=3) |  | A218411 |  |  |  |  
  | Z12 | k+5/7 | 588 (k=2) | 2520 (k=3) | 11466 (k=2) | 167580 (k=3) |  |  |  |  | A218412 |  |  |  |  
  | Z13 | k+6/7 | 168 (k=2) | 11172 (k=2) | 217854 (k=2) | 228480 (k=3) | 446880 (k=3) |  |  |  | A218413 |  |  |  |  
  |  |  |  |  |  |  
  | Z14 | k+1/8 | 58752 (k=3) | 9694080 (k=4) |  |  |  |  |  |  |  |  |  |  |  
  | Z15 | k+3/8 | 32640 (k=3) | 4840192 (k=2) |  |  |  |  |  |  |  |  |  |  |  
  | Z16 | k+5/8 | 96 (k=2) |  |  |  |  |  |  |  |  |  |  |  |  
  | Z17 | k+7/8 | 760320 (k=3) | 1468800 (k=3) | 4612608 (k=3) |  |  |  |  |  | A218429 |  |  |  |  
  |  |  |  |  |  |  
  | Z18 | k+1/9 | 540 (k=3) | 3276 (k=3) | 58032 (k=3) | 950976 (k=3) | 1862190 (k=3) |  |  |  | A218414 |  |  |  |  
  | Z19 | k+2/9 | 54 (k=2) | 2744280 (k=4) | 6191640 (k=4) |  |  |  |  |  | A218430 |  |  |  |  
  | Z20 | k+3/9 (k+1/3) | 12
  (k=2) | 234 (k=2) | 1080 (k=3) | 6048 (k=3) | 6552 (k=3) | 435708 (k=3) | 4713984 (k=3) |  | A160320 by J.C.Klein |  |  |  |  
  | Z21 | k+4/9 | 1782 (k=2) | 2160 (k=3) | 5400 (k=3) | 13104 (k=3) |  |  |  |  | A218415 |  |  |  |  
  | Z22 | k+5/9 | 3780 (k=3) | 66960 (k=3) | 167400 (k=3) | 406224 (k=3) | 1097280 (k=3) | 6656832 (k=3) | 13035330 (k=3) | 29410290 (k=3) | A218416 |  |  |  |  
  | Z23 | k+7/9 | 216 (k=2) | 2678400 (k=3) |  |  |  | A218417 |  |  |  |  
  | Z24 | k+8/9 | 252 (k=2) | 4464 (k=2) | 73152 (k=2) | 7448760 (k=3) |  |  |  |  | A218418 |  |  |  |  
  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
 
 
 
Author:  
z
(punkt)
červenka (sabáčka)
centrum
(punkt)
cz
 
 Published: 28. 10. 2012
 
 Copyright © 2012 Zdeněk Červenka
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