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

1,2

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]

Links

Table of n, a(n) for n=1..67.

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

Formula

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

Example

(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.

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 *)

Crossrefs

Cf. A106253.

Sequence in context: A338446 A190719 A187224 * A184415 A050111 A090542

Adjacent sequences: A106249 A106250 A106251 * A106253 A106254 A106255

Keyword

nonn,easy

Author

John W. Layman, Apr 27 2005

Status

approved