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A094378
Number of numbers having exactly n representations as ab+ac+bc with 0 < a < b < c.
4
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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 28 2004
STATUS
approved