A055745 Squarefree numbers not of form ab + bc + ca for 1 <= a <= b <= c (probably the list is complete).

1, 2, 6, 10, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• nice

References

• Maohua Le, A note on positive integer solutions of the equation xy+yz+zx=n, Publ. Math. Debrecen 52 (1998) 159-165; Math. Rev. 98j:11016.

Links

• J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
• J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]
• J. Borwein and K.-K. S. Choi, On the representations of xy+yz+zx, Experimental Mathematics, 9 (2000), 153-158.

Crossrefs

Cf. A034168, A025052, A034169.

Programs

Mathematica

solQ[n_, x_] := Reduce[1 <= y <= z && n == x*y + y*z + z*x, {y, z}, Integers] =!= False; solQ[n_] := Catch[xm = Ceiling[(n-1)/2]; For[x = 1, x <= xm, x++, Which[ solQ[n, x] === True, Throw[True], x == xm, Throw[False]]]] ; solQ[1] = False; Reap[ Do[ If[ SquareFreeQ[n], If[! solQ[n] , Print[n]; Sow[n]]], {n, 1, 500}]][[2, 1]] (* Jean-François Alcover, Jun 15 2012 *)