%I #16 Feb 28 2020 22:11:47
%S 2,5,3,10,4,13,2,17,9,5,7,11,26,4,29,6,3,2,37,19,13,41,7,4,9,2,50,13,
%T 53,27,5,8,19,58,4,61,2,65,33,17,3,14,9,73,74,4,11,3,82,28,85,43,89,
%U 10,4,31,2,5,97,2,101,51,21,106,4,109,11,37,16,113,57
%N Second factor in happy factorization of n-th rectangular number.
%C a(n) > 1;
%C a(n) = A007967(A007969(n)) = A007969(n) / A191854(n);
%C (A191854(n), a(n)) is a 1-happy couple;
%C notation: C in the Conway link.
%H Reinhard Zumkeller, <a href="/A191855/b191855.txt">Table of n, a(n) for n = 1..200</a>
%H J. H. Conway, <a href="http://www.cs.uwaterloo.ca/journals/JIS/happy.html">On Happy Factorizations</a>, J. Integer Sequences, Vol. 1, 1998, #1.
%t r[b_, c_] := (red = Reduce[x > 0 && y > 0 && b*x^2 + 1 == c*y^2, {x, y}, Integers] /. C[1] -> 1 // Simplify; If[Head[red] === Or, First[red], red]); f[128] = {}(* to speed up *); f[n_] := f[n] = If[IntegerQ[Sqrt[n]], {}, Do[c = n/b; If[(r0 = r[b, c]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; Return[{b, c, x0, y0}]], {b, Divisors[n] // Most}]]; A191855 = Reap[Table[Print[n, " ", f[n]]; If[f[n] != {} && f[n] =!= Null, Sow[f[n][[2]]]], {n, 1, 130}]][[2, 1]] (* _Jean-François Alcover_, Sep 18 2015 *)
%o (Haskell)
%o a191855 = a007967 . a007969 -- _Reinhard Zumkeller_, Oct 11 2015
%Y Cf. A007967, A007969, A191854.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 18 2011
%E Wrong formula removed (thanks to _Wolfdieter Lang_, who pointed this out) by _Reinhard Zumkeller_, Oct 11 2015