A212256 Number of (w,x,y,z) with all terms in {1,...,n} and 4/w = 1/x + 1/y + 1/z + 1/n.

0, 1, 1, 4, 13, 1, 22, 1, 13, 10, 22, 1, 61, 1, 18, 102, 13, 1, 82, 1, 156, 79, 1, 1, 184, 1, 1, 10, 183, 1, 297, 1, 13, 105, 1, 181, 298, 1, 1, 16, 285, 1, 378, 1, 64, 405, 1, 1, 358, 1, 37, 13, 96, 1, 163, 130, 402, 31, 1, 1, 944

Offset: 0

Author

Clark Kimberling, May 15 2012

Keywords

• nonn

Comments

w = harmonic mean of {x,y,z,n}. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[4/w == 1/x + 1/y + 1/z + 1/n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]]  (*  A212256 *)
(* Peter J. C. Moses, Apr 13 2012 *)

PARI

A212256(n) = sum(w=1,n, sum(x=1,n, sum(y=1,n, sum(z=1,n, (4/w)==((1/x)+(1/y)+(1/z)+(1/n)))))); \\ (Is there any significantly faster program?) - Antti Karttunen, Feb 15 2023