A094381 Number of numbers having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.

18, 16, 61, 30, 133, 51, 119, 48, 275, 59, 217, 72, 386, 65, 292, 83, 545, 101, 332, 89, 673, 120, 453, 106, 865, 104

Offset: 0

Author

T. D. Noe, Apr 28 2004

Keywords

• nonn

Comments

Numbers up to 250,000 were checked. Note that there seem to be many more numbers having an even number of representations. Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence.

Examples

			a(1) = 16 because there are 16 numbers (A093670) with unique representations.
		

References

• See A025052

Crossrefs

Cf. A025052 (n having no representations), A093670 (n having one representation), A094379, A094380.

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, 3]], {i, cntMax+1}]