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Number of (w,x,y,z) with all terms in {1,...,n} and w^2>=x*y*z.
3

%I #10 Dec 04 2016 19:46:29

%S 0,1,8,31,87,185,353,605,978,1471,2123,2958,4028,5308,6864,8733,10947,

%T 13491,16452,19837,23711,28047,32929,38376,44498,51181,58569,66699,

%U 75588,85260,95808,107202,119569,132821,147102,162427,178898

%N Number of (w,x,y,z) with all terms in {1,...,n} and w^2>=x*y*z.

%C a(n)+A212063(n)=n^4. For a guide to related sequences, see A211795.

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w^2 >= x*y*z, s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 50]] (* A212064 *)

%t (* _Peter J. C. Moses_, Apr 13 2012 *)

%Y Cf. A211795.

%K nonn

%O 0,3

%A _Clark Kimberling_, Apr 30 2012