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The first few terms of the full enumeration are 1, 2, 1/2, 3, 1/3, 4, 3/2, 2/3, 1/4, 5, giving a(n) = 1, 2, 4, 6, 10,...
Contribution from R. J. Mathar, Jul 20 2009: (Start)
The positions in the first column of the table
....1..1/2..1/3..1/4..1/5..1/6..1/7..1/8..1/9.1/10.1/11.1/12
....2.......2/3.......2/5.......2/7.......2/9......2/11.....
....3..3/2.......3/4..3/5.......3/7..3/8......3/10.3/11.....
....4.......4/3.......4/5.......4/7.......4/9......4/11.....
....5..5/2..5/3..5/4.......5/6..5/7..5/8..5/9......5/11.5/12
....6.................6/5.......6/7................6/11.....
....7..7/2..7/3..7/4..7/5..7/6.......7/8..7/9.7/10.7/11.7/12
....8.......8/3.......8/5.......8/7.......8/9......8/11.....
....9..9/2.......9/4..9/5.......9/7..9/8......9/10.9/11.....
...10......10/3................10/7......10/9.....10/11.....
...11.11/2.11/3.11/4.11/5.11/6.11/7.11/8.11/911/10.....11/12
...12................12/5......12/7...............12/11.....
if scanned along rising antidiagonals, as defined by the ratios A038566(i)/A020653(i). (End)
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