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A212058 Number of (w,x,y,z) with all terms in {1,...,n} and w>=x*y*z.

%I A212058 #13 Oct 05 2020 05:03:02
%S A212058 0,1,5,12,25,41,66,94,132,176,229,285,359,436,522,617,727,840,971,
%T A212058 1105,1257,1418,1588,1761,1964,2173,2391,2619,2865,3114,3390,3669,
%U A212058 3969,4278,4596,4923,5286,5652,6027,6411,6825,7242,7686,8133,8598
%N A212058 Number of (w,x,y,z) with all terms in {1,...,n} and w>=x*y*z.
%C A212058 a(n)+A212057(n)=n^4.  For a guide to related sequences, see A211795.
%F A212058 a(n) = Sum_{i=1..n+1} Sum_{j=1..n+1} tau(i)*floor((n+1-j)/i). - _Ridouane Oudra_, Oct 03 2020
%t A212058 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212058 (Do[If[w >= x*y*z, s = s + 1],
%t A212058 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212058 Map[t[#] &, Range[0, 50]] (* A212058 *)
%t A212058 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A212058 Cf. A211795, A061201.
%K A212058 nonn
%O A212058 0,3
%A A212058 _Clark Kimberling_, Apr 30 2012