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%I #6 Mar 30 2012 17:22:33
%S 65,23,91,40,197,39,195,56,298,87,217,60,512,97,327,77,562,125,433,88,
%T 712,125,484,115,924,121
%N Number of numbers having exactly n representations as ab+ac+bc with 0 < a < b < c.
%C 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.
%D See A025052
%e a(1) = 23 because there are 23 numbers (A093669) with unique representations.
%t 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}]
%Y Cf. A000926 (n having no representations), A093669 (n having one representation), A094376, A094377.
%K nonn
%O 0,1
%A _T. D. Noe_, Apr 28 2004
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