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On the other hand, in accordance with the first conjecture, 15 is in the sequence because there theare symmetricthree representationpartitions of sigma(15) = 24 into an odd number hasof widthconsecutive parts: [15], [8, 7], [5, 4, 3, 2, 1], and there is only one partition of 15 into an even onnumber theof mainconsecutive diagonalparts: [8, as7], therefore shownthe belowdifference inof the number of those partitions fourthis quadrant:3 - 1 = 2.
On the other hand, in accordance with the second conjecture, 15 is in the sequence because the symmetric representation of sigma(15) = 24 has width 2 on the main diagonal, as shown below in the fourth quadrant:
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On the other hand, in accordance with the second conjecture, 15 is in the sequence because there are three partitions of 15 into an odd number of consecutive parts: [15], [8, 7], [5, 4, 3, 2, 1], and there is only one partition of 15 into an even number of consecutive parts: [8, 7], therefore the difference of the number of those partitions is 3 - 1 = 2.
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