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

1, 11, 23, 41, 47, 59, 71, 116, 119, 131, 164, 425, 191, 236, 239, 446, 335, 419, 311, 404, 431, 584, 647, 524, 479, 1019, 831, 776, 671, 944, 719, 1076, 839, 1004, 959, 1889, 1196, 2099, 1271, 1856, 1151, 1931, 1391, 1676, 1319, 1616, 1751, 3275, 1511

Offset: 0

Author

T. D. Noe and Robert G. Wilson v, Apr 28 2004

Keywords

• nonn

Comments

Note that the Mathematica program computes A094376, A094377 and A094378, but outputs only this sequence.

Examples

			a(2) = 23 because 23 is the least number with 2 representations: (a,b,c) = (1,2,7) and (1,3,5).
		

References

• See A025052

Links

• Robert Israel, Table of n, a(n) for n = 0..826

Crossrefs

Cf. A000926 (n having no representations), A093669 (n having one representation), A025052, A094377, A094378.

Programs

Maple

f:= proc(n) local a, t, s;
  t:= 0;
  for a from 1 to floor(sqrt(n/3)) do
    t:= t + nops(select(s -> s > 2*a and n+a^2 > s^2, numtheory:-divisors(n+a^2)))
  od;
  t
end proc:
N:= 200: # for a(0)..a(N)
V:= Array(0..N): count:= 0:
for n from 1 while count < N+1 do
   v:= f(n); if v <= N and V[v] = 0 then
      count:= count+1; V[v]:= n; fi
od:
seq(V[i],i=0..N); # Robert Israel, May 05 2021

Mathematica

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}]