A093670 Numbers having a unique representation as ab+ac+bc, with 1 <= a <= b <= c.

3, 5, 7, 8, 9, 12, 13, 14, 16, 25, 28, 34, 37, 46, 82, 142

Offset: 1

Author

T. D. Noe, Apr 08 2004

Keywords

• nonn

Comments

Are there more terms?

Examples

			25 is on the list because 25 = 1*1 + 1*12 + 1*12.
		

References

• See A025052

Crossrefs

Cf. A025052 (numbers not of the form ab+ac+bc, 1<=a<=b<=c).

Programs

Mathematica

oneSol={}; Do[lim=Ceiling[(n-1)/2]; cnt=0; Do[If[n>a*b && Mod[n-a*b, a+b]==0 && Quotient[n-a*b, a+b]>=b, cnt++; If[cnt>1, Break[]]], {a, 1, lim}, {b, a, lim}]; If[cnt==1, AppendTo[oneSol, n]], {n, 10000}]; oneSol