[seqfan] Regular maicable k-uples that follow a specific construction pattern

michel.marcus at free.fr michel.marcus at free.fr
Sun Dec 15 17:04:43 CET 2013


Hi S eqfans, 

Explanations 
(220, 284) is a regular pair. 
gcd is 4 
220=4*55 and 284=4*71 
other x with sigma(x) are: [30, 46, 51, 55, 71] 
55 and 71 are the 2 greatest integers of these x's. 
============================================ 
[220, 284], 504 
= 4 [55, 71] 
sigma : [72, 72] 
by [30, 46, 51, 55, 71] 
============================================ 
[289855488, 294168576, 296564736], 880588800 
= 79872 [3629, 3683, 3713] 
sigma : [3840, 3840, 3840] 
by [1674, 1736, 1995, 2079, 2558, 2607, 2679, 2697, 2765, 2945, 3059, 3353, 3629, 3683, 3713] 
============================================= 
[138710880, 153080928, 155475936, 167450976], 614718720 
= 199584 [695, 767, 779, 839] 
sigma : [840, 840, 840, 840] 
by [312, 348, 380, 494, 695, 767, 779, 839] 
============================================= 
[227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800], 1160492902900531200 
= 169390293811200 [1343, 1349, 1357, 1363, 1439] 
sigma : [1440, 1440, 1440, 1440, 1440] 
by [552, 570, 594, 616, 790, 826, 874, 885, 957, 958, 969, 1015, 1045, 1077, 1195, 1253, 1343, 1349, 1357, 1363, 1439] 
============================================= 
[8227672004190010724352000, 8316395804494798884864000, 8379378749155605295104000, 8439075627138456588288000, 8528894783002563121152000, 8587496305426096041984000] 
= 91279629943197696000 [90137, 91109, 91799, 92453, 93437, 94079] 
sigma : [94080, 94080, 94080, 94080, 94080, 94080] 
by [30996, 31668, 32292, 32604, 34580, 35196, 36666, 37284, 37608, 38076, 383 64, 
38868, 40308, 42812, 44156, 44780, 45188, 45978, 46436, 46748, 50168, 51956, 
 52628, 52772, 54866, 55377, 58214, 58617, 58785, 59073, 59546, 59631, 60237, 
60 819, 61503, 61719, 61994, 63245, 63477, 64505, 69441, 69549, 69639, 70889, 76349 
, 78071, 78395, 80759, 84071, 84293, 84929, 85241, 86621, 87203, 87347, 89357, 9 0137, 
91109, 91799, 92453, 93437, 94079] 
============================================= 

Best 
Michel


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