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

0, 1, 5, 12, 25, 41, 66, 94, 132, 176, 229, 285, 359, 436, 522, 617, 727, 840, 971, 1105, 1257, 1418, 1588, 1761, 1964, 2173, 2391, 2619, 2865, 3114, 3390, 3669, 3969, 4278, 4596, 4923, 5286, 5652, 6027, 6411, 6825, 7242, 7686, 8133, 8598

Offset: 0

Author

Clark Kimberling, Apr 30 2012

Keywords

• nonn

Comments

a(n)+A212057(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A061201.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212058 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Formula

a(n) = Sum_{i=1..n+1} Sum_{j=1..n+1} tau(i)*floor((n+1-j)/i). - Ridouane Oudra, Oct 03 2020