A092249 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).

1, 2, 4, 6, 10, 12, 18, 22, 28, 32, 42, 46, 58, 64, 72, 80, 96, 102, 120, 128, 140, 150, 172, 180, 200, 212, 230, 242, 270, 278, 308, 324, 344, 360, 384, 396, 432, 450, 474, 490, 530, 542, 584, 604, 628, 650, 696, 712, 754, 774, 806, 830, 882, 900, 940, 964

Offset

1,2

Comments

A002088 without the leading zero. [R. J. Mathar, Jul 20 2009]

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Example

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)

Mathematica

Accumulate[EulerPhi[Range[100]]] (* Paolo Xausa, Oct 19 2023 *)

Crossrefs

Cf. A000010, A002088, A020653, A038566.

Sequence in context: A152919 A306564 A002088 * A019332 A002491 A045958

Adjacent sequences: A092246 A092247 A092248 * A092250 A092251 A092252

Keyword

nonn

Author

Andrew Niedermaier, Feb 20 2004

Extensions

a(11) and a(12) corrected by R. J. Mathar, Jul 20 2009

Incorrect recurrence formula removed by R. J. Mathar, Jul 29 2009

More terms (using A002088) from Michel Marcus, Sep 10 2018

Status

approved