A106252 Number of positive integer triples (x,y,z), with x<=y<=z<=n, such that each of x,y and z divides the sum of the other two.

1, 3, 5, 7, 8, 11, 12, 14, 16, 18, 19, 22, 23, 25, 27, 29, 30, 33, 34, 36, 38, 40, 41, 44, 45, 47, 49, 51, 52, 55, 56, 58, 60, 62, 63, 66, 67, 69, 71, 73, 74, 77, 78, 80, 82, 84, 85, 88, 89, 91, 93, 95, 96, 99, 100, 102, 104, 106, 107, 110, 111, 113, 115, 117, 118, 121, 122

Offset: 1

Author

John W. Layman, Apr 27 2005

Keywords

• nonn
• easy

Comments

The following conjecture is probably not very difficult: Conjecture. The sequence (A106253) of differences of this sequence is periodic with period 6.

That the difference sequence in the above conjecture is periodic follows from a formula in the Formula and Mathematica sections; see A211701 for a discussion. [Clark Kimberling, Apr 20 2012]

Examples

			(1,1,1), (1,1,2), (1,2,3), (2,2,2) and (3,3,3) are the triples that have the desired property for n=3, so a(3)=5.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 0, -1).

Crossrefs

Cf. A106253.

Programs

Mathematica

f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]; t = Table[f[n, 3], {n, 1, 90}] (* Clark Kimberling, Apr 20 2012 *)
LinearRecurrence[{0,1,1,0,-1},{1,3,5,7,8},67] (* Ray Chandler, Aug 01 2015 *)

Formula

a(n) = n + floor(n/2) + floor(n/3). [Clark Kimberling, Apr 20 2012]