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

0,1

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.

References

See A025052

Links

Table of n, a(n) for n=0..25.

Example

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

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}]

Crossrefs

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

Sequence in context: A079293 A070646 A375676 * A375675 A074972 A118511

Adjacent sequences: A094378 A094379 A094380 * A094382 A094383 A094384

Keyword

nonn

Author

T. D. Noe, Apr 28 2004

Status

approved