cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A341316 Row sums in A341315.

Original entry on oeis.org

0, 3, 6, 12, 18, 33, 33, 66, 66, 93, 96, 168, 117, 237, 195, 222, 258, 411, 276, 516, 348, 453, 501, 762, 453, 783, 708, 822, 711, 1221, 663, 1398, 1026, 1167, 1230, 1356, 1008, 2001, 1545, 1650, 1356, 2463, 1356, 2712, 1833, 1923, 2283, 3246, 1797, 3153, 2346, 2868, 2592, 4137
Offset: 0

Views

Author

N. J. A. Sloane, Feb 17 2021

Keywords

Comments

This is three times A057661. See that entry for much more information.

Crossrefs

Formula

a(n) = 3*(A057660(n)+1)/2 for n>=1. - Hugo Pfoertner, Feb 17 2021

A341314 Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 2, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 3, 2, 3, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 4, 8, 2, 8, 4, 8, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 1
Offset: 0

Views

Author

N. J. A. Sloane, Feb 17 2021

Keywords

Comments

We define gcd(0,0) = 0.
This sequence arose when studying Reed Kelly's A214551.

Examples

			The array begins:
  0,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
  1,  3,  2,  5,  3,  7,  4,  9,  5, 11,  6, 13,  7, ...
  1,  4,  5,  2,  7,  8,  3, 10, 11,  4, 13, 14,  5, ...
  1,  5,  3,  7,  2,  9,  5, 11,  3, 13,  7, 15,  4, ...
  1,  6,  7,  8,  9,  2, 11, 12, 13, 14,  3, 16, 17, ...
  1,  7,  4,  3,  5, 11,  2, 13,  7,  5,  8, 17,  3, ...
  1,  8,  9, 10, 11, 12, 13,  2, 15, 16, 17, 18, 19, ...
  1,  9,  5, 11,  3, 13,  7, 15,  2, 17,  9, 19,  5, ...
  1, 10, 11,  4, 13, 14,  5, 16, 17,  2, 19, 20,  7, ...
  1, 11,  6, 13,  7,  3,  8, 17,  9, 19,  2, 21, 11, ...
  1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,  2, 23, ...
  1, 13,  7,  5,  4, 17,  3, 19,  5,  7, 11, 23,  2, ...
...
The first few antidiagonals are:
  [0]
  [1, 1]
  [1, 2, 1]
  [1, 3, 3, 1]
  [1, 4, 2, 4, 1]
  [1, 5, 5, 5, 5, 1]
  [1, 6, 3, 2, 3, 6, 1]
  [1, 7, 7, 7, 7, 7, 7, 1]
  [1, 8, 4, 8, 2, 8, 4, 8, 1]
  ...
		

Crossrefs

A054531 is a similar sequence. See also A341315, A341316.
Cf. A214551.

Programs

  • Maple
    fa:= (m,n) -> if m=0 and n=0 then 0 else (m+n)/igcd(m,n); fi;
    for m from 0 to 12 do lprint([seq(fa(m-n,n),n=0..m)]); od:
    for m from 0 to 12 do lprint([seq(fa(m,n),n=0..12)]); od:
Showing 1-2 of 2 results.