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

%I A212256 #11 Feb 15 2023 14:04:17
%S A212256 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,
%T A212256 1,10,183,1,297,1,13,105,1,181,298,1,1,16,285,1,378,1,64,405,1,1,358,
%U A212256 1,37,13,96,1,163,130,402,31,1,1,944
%N A212256 Number of (w,x,y,z) with all terms in {1,...,n} and 4/w = 1/x + 1/y + 1/z + 1/n.
%C A212256 w = harmonic mean of {x,y,z,n}.  For a guide to related sequences, see A211795.
%t A212256 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212256 (Do[If[4/w == 1/x + 1/y + 1/z + 1/n, s = s + 1],
%t A212256 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212256 Map[t[#] &, Range[0, 60]]  (*  A212256 *)
%t A212256 (* _Peter J. C. Moses_, Apr 13 2012 *)
%o A212256 (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
%Y A212256 Cf. A211795.
%K A212256 nonn
%O A212256 0,4
%A A212256 _Clark Kimberling_, May 15 2012