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A212067 Number of (w,x,y,z) with all terms in {1,...,n} and w^3 = x*y*z.

%I A212067 #12 Dec 04 2016 19:46:29
%S A212067 0,1,2,3,10,11,12,13,26,45,46,47,60,61,62,63,88,89,120,121,128,129,
%T A212067 130,131,162,199,200,255,262,263,264,265,332,333,334,335,402,403,404,
%U A212067 405,436,437,438,439,446,477,478,479,540,601,674,675,682,683,786
%N A212067 Number of (w,x,y,z) with all terms in {1,...,n} and w^3 = x*y*z.
%C A212067 For a guide to related sequences, see A211795.
%H A212067 Chai Wah Wu, <a href="/A212067/b212067.txt">Table of n, a(n) for n = 0..10000</a>
%e A212067 G.f. = x + 2*x^2 + 3*x^3 + 10*x^4 + 11*x^5 + 12*x^6 + 13*x^7 + 26*x^8 + ...
%e A212067 a(4) counts these ten 4-tuples:
%e A212067 (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4),
%e A212067 (2,1,2,4), (2,1,4,2), (2,2,1,4), (2,2,4,1),
%e A212067 (2,4,1,2), (2,4,2,1).
%t A212067 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212067 (Do[If[w^3 == x*y*z, s = s + 1],
%t A212067 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212067 Map[t[#] &, Range[0, 60]] (* A212067 *)
%t A212067 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A212067 a[ n_] := Length@FindInstance[ w^3 == x y z && 0 < w <= n && 0 < x <= n && 0 < y <= n && 0 < z <= n, {w, x, y, z}, Integers, 10^9]; (* _Michael Somos_, Nov 26 2016 *)
%Y A212067 Cf. A211795, A212068.
%K A212067 nonn
%O A212067 0,3
%A A212067 _Clark Kimberling_, Apr 30 2012