A094378 Number of numbers having exactly n representations as ab+ac+bc with 0 < a < b < c.

65, 23, 91, 40, 197, 39, 195, 56, 298, 87, 217, 60, 512, 97, 327, 77, 562, 125, 433, 88, 712, 125, 484, 115, 924, 121

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

References

See A025052

Links

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

Example

a(1) = 23 because there are 23 numbers (A093669) with unique representations.

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

Crossrefs

Cf. A000926 (n having no representations), A093669 (n having one representation), A094376, A094377.

Sequence in context: A034061 A113696 A302210 * A033385 A275484 A297941

Adjacent sequences: A094375 A094376 A094377 * A094379 A094380 A094381

Keyword

nonn

Author

T. D. Noe, Apr 28 2004

Status

approved