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A094379 Least number having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.

%I A094379 #12 Jul 13 2013 12:03:13
%S A094379 1,3,11,23,35,47,59,71,95,188,119,164,231,191,215,239,299,356,335,311,
%T A094379 404,431,591,584,524,479,551,656,831,776,671,719,791,839,1004,1031,
%U A094379 959,1244,1196,1439,1271,1151,1931,1847,1391,1319,1811,1784,1616,1511,1799
%N A094379 Least number having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.
%C A094379 Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence.
%C A094379 A066955(a(n)) = n and A066955(m) = n for m < a(n). [_Reinhard Zumkeller_, Mar 23 2012]
%D A094379 See A025052
%H A094379 Reinhard Zumkeller, <a href="/A094379/b094379.txt">Table of n, a(n) for n = 0..125</a>
%e A094379 a(3) = 23 because 23 is the least number with 3 representations: (a,b,c) = (1,1,11), (1,2,7) and (1,3,5).
%t A094379 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, 1]], {i, cntMax+1}]
%o A094379 (Haskell)
%o A094379 import Data.List (elemIndex)
%o A094379 import Data.Maybe (fromJust)
%o A094379 a094379 = (+ 1) . fromJust . (`elemIndex` a066955_list)
%o A094379 -- _Reinhard Zumkeller_, Mar 23 2012
%Y A094379 Cf. A025052 (n having no representations), A093670 (n having one representation), A094380, A094381.
%K A094379 nonn
%O A094379 0,2
%A A094379 _T. D. Noe_, Apr 28 2004