A094377 - OEIS

%I #16 Oct 01 2017 13:14:07

%S 1848,193,1012,862,3040,2062,4048,3217,7392,4162,7837,8002,12397,

%T 13297,14722,16417,21253,21058,30493,27358,34357,34318,47338,40177,

%U 50317,39502,61462,62302,73117,83218,106177,67138,92698,102958,134773,111577,112942,121522,104938,96958,151237,166798,150382,139393,190513,129838

%N Greatest number having exactly n representations as ab+ac+bc with 0 < a < b < c.

%C Numbers up to 250,000 were checked. Note that the Mathematica program computes A094376, A094377 and A094378, but outputs only this sequence.

%D See A025052.

%e a(1) = 193 because 193 is the largest number with a unique representation: (a,b,c) = (4,7,15).

%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, 2]], {i, cntMax+1}]

%Y Cf. A000926 (n having no representations), A093669 (n having one representation), A094376, A094378.

%K nonn

%O 0,1

%A _T. D. Noe_, Apr 28 2004

%E More terms (using limit 10^6) from _Joerg Arndt_, Oct 01 2017