A094380 Greatest number having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.

462, 142, 742, 862, 2170, 2062, 3502, 2962, 5278, 5413, 7282, 8002, 11302, 11278, 14722, 13918, 18778, 21058, 30178, 30493, 30622, 34318, 47338, 31102, 44902, 43717

Offset: 0

Author

T. D. Noe, Apr 28 2004

Keywords

• nonn

Comments

Numbers up to 250,000 were checked. Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence.

Examples

			a(1) = 142 because 142 is the largest number with a unique representation: (a,b,c) = (1,10,12).
		

References

• See A025052

Crossrefs

Cf. A025052 (n having no representations), A093670 (n having one representation), A094379, A094381.

Programs

Mathematica

cntMax=10; nSol=Table[{0, 0, 0}, {cntMax+1}]; 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>cntMax, Break[]]], {a, 1, lim}, {b, a, lim}]; If[cnt<=cntMax, If[nSol[[cnt+1, 1]]==0, nSol[[cnt+1, 1]]=n]; nSol[[cnt+1, 2]]=n; nSol[[cnt+1, 3]]++;], {n, 10000}]; Table[nSol[[i, 2]], {i, cntMax+1}]