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

0, 1, 2, 3, 10, 11, 12, 13, 26, 45, 46, 47, 60, 61, 62, 63, 88, 89, 120, 121, 128, 129, 130, 131, 162, 199, 200, 255, 262, 263, 264, 265, 332, 333, 334, 335, 402, 403, 404, 405, 436, 437, 438, 439, 446, 477, 478, 479, 540, 601, 674, 675, 682, 683, 786

Offset: 0

Author

Clark Kimberling, Apr 30 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211795.

Examples

			G.f. = x + 2*x^2 + 3*x^3 + 10*x^4 + 11*x^5 + 12*x^6 + 13*x^7 + 26*x^8 + ...
a(4) counts these ten 4-tuples:
(1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4),
(2,1,2,4), (2,1,4,2), (2,2,1,4), (2,2,4,1),
(2,4,1,2), (2,4,2,1).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A211795, A212068.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^3 == x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]] (* A212067 *)
(* Peter J. C. Moses, Apr 13 2012 *)
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 *)