A341315 Triangle read by rows: T(n,k) = (n+k)/gcd(n,k), n>=0, 0<=k<=n.

0, 1, 2, 1, 3, 2, 1, 4, 5, 2, 1, 5, 3, 7, 2, 1, 6, 7, 8, 9, 2, 1, 7, 4, 3, 5, 11, 2, 1, 8, 9, 10, 11, 12, 13, 2, 1, 9, 5, 11, 3, 13, 7, 15, 2, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2, 1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2

Offset

0,3

Comments

We define gcd(0,0) = 0.

This is half of the array A341314. See that entry for further information.

Links

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

Example

Triangle begins:
  [0]
  [1,  2]
  [1,  3,  2]
  [1,  4,  5,  2]
  [1,  5,  3,  7,  2]
  [1,  6,  7,  8,  9,  2]
  [1,  7,  4,  3,  5, 11,  2]
  [1,  8,  9, 10, 11, 12, 13,  2]
  [1,  9,  5, 11,  3, 13,  7, 15,  2]
  [1, 10, 11,  4, 13, 14,  5, 16, 17,  2]
  [1, 11,  6, 13,  7,  3,  8, 17,  9, 19, 2]
  [1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2]
  ...

Crossrefs

Cf. A341314. A054531 is essentially the same triangle.

See A341316 for the row sums.

Sequence in context: A108786 A008315 A191318 * A293600 A191395 A183917

Adjacent sequences: A341312 A341313 A341314 * A341316 A341317 A341318

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 17 2021

Status

approved