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A341314 Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

We define gcd(0,0) = 0.

This sequence arose when studying Reed Kelly's A214551.

LINKS

Table of n, a(n) for n=0..90.

EXAMPLE

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]

  ...

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:

CROSSREFS

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

Cf. A214551.

Sequence in context: A225043 A125605 A110570 * A335174 A082905 A141524

Adjacent sequences:  A341311 A341312 A341313 * A341315 A341316 A341317

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 17 2021

STATUS

approved

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Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)