A212103 Number of (w,x,y,z) with all terms in {1,...,n} and w = harmonic mean of {x,y,z}.

0, 1, 2, 3, 10, 11, 30, 31, 38, 39, 52, 53, 84, 85, 86, 117, 124, 125, 144, 145, 200, 225, 226, 227, 282, 283, 284, 285, 334, 335, 420, 421, 428, 435, 436, 491, 546, 547, 548, 555, 634, 635, 726, 727, 758, 837, 838, 839, 936, 937, 956, 957, 970, 971

Offset

0,3

Comments

Also, the number of (w,x,y,z) with all terms in {1,...,n} and H(w,x,y)=H(w,x,y,z) where H denotes harmonic mean. For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..53.

Example

a(4) counts these:  (1,1,1,1), (2,1,4,4), (2,2,2,2), (2,4,1,4), (2,4,4,1), (3,2,4,4), (3,3,3,3), (3,4,2,4), (3,4,4,2), (4,4,4,4); e.g., (3,2,4,4) is included because it satisfies 3/w=1/x+1/y+1/z.

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*(y*z + z*x + x*y) == 3 x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]] (* A212103 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795.

Sequence in context: A324921 A307034 A081868 * A193652 A345369 A092986

Adjacent sequences: A212100 A212101 A212102 * A212104 A212105 A212106

Keyword

nonn

Author

Clark Kimberling, May 03 2012

Status

approved