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%I #5 Mar 30 2012 17:22:33
%S 462,142,742,862,2170,2062,3502,2962,5278,5413,7282,8002,11302,11278,
%T 14722,13918,18778,21058,30178,30493,30622,34318,47338,31102,44902,
%U 43717
%N Greatest number having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.
%C Numbers up to 250,000 were checked. Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence.
%D See A025052
%e a(1) = 142 because 142 is the largest number with a unique representation: (a,b,c) = (1,10,12).
%t 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, 2]], {i, cntMax+1}]
%Y Cf. A025052 (n having no representations), A093670 (n having one representation), A094379, A094381.
%K nonn
%O 0,1
%A _T. D. Noe_, Apr 28 2004
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