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A094376 Least number having exactly n representations as ab+ac+bc with 0 < a < b < c.

%I A094376 #10 May 05 2021 20:52:41
%S A094376 1,11,23,41,47,59,71,116,119,131,164,425,191,236,239,446,335,419,311,
%T A094376 404,431,584,647,524,479,1019,831,776,671,944,719,1076,839,1004,959,
%U A094376 1889,1196,2099,1271,1856,1151,1931,1391,1676,1319,1616,1751,3275,1511
%N A094376 Least number having exactly n representations as ab+ac+bc with 0 < a < b < c.
%C A094376 Note that the Mathematica program computes A094376, A094377 and A094378, but outputs only this sequence.
%D A094376 See A025052
%H A094376 Robert Israel, <a href="/A094376/b094376.txt">Table of n, a(n) for n = 0..826</a>
%e A094376 a(2) = 23 because 23 is the least number with 2 representations: (a,b,c) = (1,2,7) and (1,3,5).
%p A094376 f:= proc(n) local a, t, s;
%p A094376   t:= 0;
%p A094376   for a from 1 to floor(sqrt(n/3)) do
%p A094376     t:= t + nops(select(s -> s > 2*a and n+a^2 > s^2, numtheory:-divisors(n+a^2)))
%p A094376   od;
%p A094376   t
%p A094376 end proc:
%p A094376 N:= 200: # for a(0)..a(N)
%p A094376 V:= Array(0..N): count:= 0:
%p A094376 for n from 1 while count < N+1 do
%p A094376    v:= f(n); if v <= N and V[v] = 0 then
%p A094376       count:= count+1; V[v]:= n; fi
%p A094376 od:
%p A094376 seq(V[i],i=0..N); # _Robert Israel_, May 05 2021
%t A094376 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, 1]], {i, cntMax+1}]
%Y A094376 Cf. A000926 (n having no representations), A093669 (n having one representation), A025052, A094377, A094378.
%K A094376 nonn
%O A094376 0,2
%A A094376 _T. D. Noe_ and _Robert G. Wilson v_, Apr 28 2004