

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.


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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: A195439 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



