A214646 a(n) = (a(n-2) + a(n-3))/gcd(a(n-2), a(n-3)) with a(1) = a(2) = a(3) = 1.

1, 1, 1, 2, 2, 3, 2, 5, 5, 7, 2, 12, 9, 7, 7, 16, 2, 23, 9, 25, 32, 34, 57, 33, 91, 30, 124, 121, 77, 245, 18, 46, 263, 32, 309, 295, 341, 604, 636, 945, 310, 527, 251, 27, 778, 278, 805, 528, 1083, 1333, 537, 2416, 1870, 2953, 2143, 4823, 5096, 6966, 109

Offset: 1

Author

Reed Kelly, Jul 24 2012

Keywords

• nonn

Comments

A variation on A214551 with the second and third terms being added and divided by the greatest common divisor of the pair of numbers.

Examples

			a(6) = (a(4)+a(3))/gcd(a(4),a(3)) = (2+1)/1 = 3.
a(19) = (a(17)+a(16))/gcd(a(17),a(16)) = (2+16)/2 = 9.
		

Links

• Reed Kelly, Table of n, a(n) for n = 1..1003

Crossrefs

Cf. A214551, A000931.

Programs

Mathematica

DivGCDxy[n_, x_, y_, init_] := Module[{t, a, i}, t = init;
  Do[AppendTo[t, (t[[-x]] + t[[-y]])/GCD[t[[-x]], t[[-y]]]], {n}];
  t]; DivGCDxy[100, 2, 3, {1, 1, 1}]

Extensions

NAME adapted to offset and b-file. - R. J. Mathar, Jun 19 2021