A212107 Number of (w,x,y,z) with all terms in {1,...,n} and w >= harmonic mean of {x,y,z}.

0, 1, 9, 48, 160, 384, 798, 1468, 2517, 4041, 6172, 9063, 12870, 17746, 23907, 31581, 40933, 52227, 65721, 81676, 100401, 122136, 147205, 175944, 208716, 245833, 287685, 334665, 387211, 445701, 510642, 582343, 661380, 748185, 843286

Offset: 0

Author

Clark Kimberling, May 04 2012

Keywords

• nonn

Comments

a(n)+A212106(n)=n^4.

A 4-tuple (w,x,y,z) is counted if 3/w>=1/x+1/y+1/z.

For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A212103.

Programs

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, 40]] (* A212107 *)
(* Peter J. C. Moses, Apr 13 2012 *)