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%I #7 Feb 05 2018 15:18:15
%S 2,6,12,14,24,26,30,28,48,50,54,62,52,58,96,56,60,98,102,110,126,100,
%T 106,118,192,104,108,194,114,122,198,206,222,254,112,124,116,196,202,
%U 214,238,384,120,200,204,386,210,218,390,230,246,398,414,446,510
%N Irregular table of natural numbers (read by columns) which can be mapped to the source partitions described in A053445 and A126441.
%C Sequences A000041, A002865 and A053445 count numeric partitions. A125106 maps numeric partitions to the natural numbers and has A000120 elements per row. A126441 has A000041 elements per column and is a tabular arrangement of the natural numbers. A140691 is a rearrangement of table A126441. A140692 extracts the cyclic cases and has A002865 elements per column.
%C The values for A140760 can also be generated by beginning with A140759 and repeatedly multiplying by two as follows:
%C 2
%C ....6.....12......24.....48.....96
%C ..........14..........28........56
%C ..................26........52....
%C ..................30............60
%C .........................50.......
%C .........................54.......
%C .........................62.......
%C Note that the number of entries in each column is given by A053445.
%e The values of A140760 can be obtained by selecting the first even number on each applicable row of Table A126441.
%e Table A126441 begins
%e 1.2.4..8.16.32.64.128.256.512.1024
%e ..3.5..9.17.33.65.129.257.513.1025
%e .......6.10.18.34..66.130.258..514
%e ....7.11.19.35.67.131.259.515.1027
%e ............12.20..36..68.132..260
%e .........13.21.37..69.133.261..517
%e ............14.22..38..70.134..262
%e ......15.23.39.71.135.263.519.1031
%e ...................24..40..72..136
%e ...............25..41..73.137..265
%e ...................26..42..74..138
%e ............27.43..75.139.267..523
%e .......................28..44...76
%e ...............29..45..77.141..269
%e ...................30..46..78..142
%e .........31.47.79.143.271.527.1039
%e ...........................48...80
%e .......................49..81..145
%e ...........................50...82
%e ...................51..83.147..275
%Y Cf. A000041, A000120, A002865, A053445, A125106, A126441, A140691, A140692, A140759.
%K nonn,tabf
%O 1,1
%A _Alford Arnold_, May 28 2008
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