A094377 Greatest number having exactly n representations as ab+ac+bc with 0 < a < b < c.

1848, 193, 1012, 862, 3040, 2062, 4048, 3217, 7392, 4162, 7837, 8002, 12397, 13297, 14722, 16417, 21253, 21058, 30493, 27358, 34357, 34318, 47338, 40177, 50317, 39502, 61462, 62302, 73117, 83218, 106177, 67138, 92698, 102958, 134773, 111577, 112942, 121522, 104938, 96958, 151237, 166798, 150382, 139393, 190513, 129838

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 A094376, A094377 and A094378, but outputs only this sequence.

Examples

			a(1) = 193 because 193 is the largest number with a unique representation: (a,b,c) = (4,7,15).
		

References

• See A025052.

Crossrefs

Cf. A000926 (n having no representations), A093669 (n having one representation), A094376, A094378.

Programs

Mathematica

cntMax=10; nSol=Table[{0, 0, 0}, {cntMax+1}]; Do[lim=Ceiling[(n-2)/3]; 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-1}, {b, a+1, 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}]

Extensions

More terms (using limit 10^6) from Joerg Arndt, Oct 01 2017