

A055745


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


2



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

1,2


REFERENCES

Maohua Le, A note on positive integer solutions of the equation xy+yz+zx=n, Publ. Math. Debrecen 52 (1998) 159165; Math. Rev. 98j:11016.


LINKS

Table of n, a(n) for n=1..16.
J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 70th [Birthday] Meeting, 2015, revised May 2016.
J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 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), 153158 (dvi, ps).


MATHEMATICA

solQ[n_, x_] := Reduce[1 <= y <= z && n == x*y + y*z + z*x, {y, z}, Integers] =!= False; solQ[n_] := Catch[xm = Ceiling[(n1)/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]] (* JeanFrançois Alcover, Jun 15 2012 *)


CROSSREFS

Cf. A034168, A025052, A034169.
Sequence in context: A077064 A080715 A034168 * A182000 A167512 A055895
Adjacent sequences: A055742 A055743 A055744 * A055746 A055747 A055748


KEYWORD

nonn,fini,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



