A212060 Number of (w,x,y,z) with all terms in {1,...,n} and w=x*y*z-2.

0, 0, 3, 6, 15, 18, 28, 34, 43, 46, 64, 67, 76, 85, 100, 103, 121, 124, 142, 151, 160, 163, 193, 199, 208, 218, 236, 239, 266, 269, 290, 299, 308, 317, 353, 356, 365, 374, 404, 407, 434, 437, 455, 473, 482, 485, 530, 536, 554, 563, 581, 584, 614, 623

Offset: 0

Author

Clark Kimberling, Apr 30 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211795.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A211795.

Programs

Maple

N:= 100:
A:= Vector(N):
for x from 1 to N do
  for y from 1 to min(N,floor((N+2)/x)) do
    for z from max(1,ceil(3/(x*y))) to min(N,floor((N+2)/(x*y))) do
  w:=max(x,y,z,x*y*z-2);
  A[w]:= A[w]+1;
od od od:
B:= ListTools:-PartialSums(convert(A,list)):
0,op(B); # Robert Israel, Oct 23 2019

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == x*y*z - 2, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]] (* A212060 *)
(* Peter J. C. Moses, Apr 13 2012 *)