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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)