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%I #20 Oct 19 2023 16:23:36
%S 1,2,4,6,10,12,18,22,28,32,42,46,58,64,72,80,96,102,120,128,140,150,
%T 172,180,200,212,230,242,270,278,308,324,344,360,384,396,432,450,474,
%U 490,530,542,584,604,628,650,696,712,754,774,806,830,882,900,940,964
%N Positions of the integers in the standard diagonal enumeration of the rationals (with the integers in the first column and diagonals moving up to the right).
%C A002088 without the leading zero. [_R. J. Mathar_, Jul 20 2009]
%H Paolo Xausa, <a href="/A092249/b092249.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%e 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,...
%e Contribution from _R. J. Mathar_, Jul 20 2009: (Start)
%e The positions in the first column of the table
%e ....1..1/2..1/3..1/4..1/5..1/6..1/7..1/8..1/9.1/10.1/11.1/12
%e ....2.......2/3.......2/5.......2/7.......2/9......2/11.....
%e ....3..3/2.......3/4..3/5.......3/7..3/8......3/10.3/11.....
%e ....4.......4/3.......4/5.......4/7.......4/9......4/11.....
%e ....5..5/2..5/3..5/4.......5/6..5/7..5/8..5/9......5/11.5/12
%e ....6.................6/5.......6/7................6/11.....
%e ....7..7/2..7/3..7/4..7/5..7/6.......7/8..7/9.7/10.7/11.7/12
%e ....8.......8/3.......8/5.......8/7.......8/9......8/11.....
%e ....9..9/2.......9/4..9/5.......9/7..9/8......9/10.9/11.....
%e ...10......10/3................10/7......10/9.....10/11.....
%e ...11.11/2.11/3.11/4.11/5.11/6.11/7.11/8.11/911/10.....11/12
%e ...12................12/5......12/7...............12/11.....
%e if scanned along rising antidiagonals, as defined by the ratios A038566(i)/A020653(i). (End)
%t Accumulate[EulerPhi[Range[100]]] (* _Paolo Xausa_, Oct 19 2023 *)
%Y Cf. A000010, A002088, A020653, A038566.
%K nonn
%O 1,2
%A _Andrew Niedermaier_, Feb 20 2004
%E a(11) and a(12) corrected by _R. J. Mathar_, Jul 20 2009
%E Incorrect recurrence formula removed by _R. J. Mathar_, Jul 29 2009
%E More terms (using A002088) from _Michel Marcus_, Sep 10 2018