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URL: https://oeis.org/A191854

⇱ A191854 - OEIS

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A191854
First factor in happy factorization of n-th rectangular number.
7
1, 1, 2, 1, 3, 1, 7, 1, 2, 4, 3, 2, 1, 7, 1, 5, 11, 17, 1, 2, 3, 1, 6, 11, 5, 23, 1, 4, 1, 2, 11, 7, 3, 1, 15, 1, 31, 1, 2, 4, 23, 5, 8, 1, 1, 19, 7, 26, 1, 3, 1, 2, 1, 9, 23, 3, 47, 19, 1, 49, 1, 2, 5, 1, 27, 1, 10, 3, 7, 1, 2, 4, 9, 2, 1, 31, 1, 14, 3, 1
OFFSET
1,3
COMMENTS
a(n) = A007966(A007969(n)) = A007969(n) / A191855(n);
(a(n), A191855(n)) is a 1-happy couple;
notation: B in the Conway link.
LINKS
J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.
MATHEMATICA
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}]]; A191854 = Reap[Table[Print[n, " ", f[n]]; If[f[n] != {} && f[n] =!= Null, Sow[f[n][[1]]]], {n, 1, 130}]][[2, 1]] (* Jean-François Alcover, Sep 18 2015 *)
PROG
(Haskell)
a191854 = a007966 . a007969 -- Reinhard Zumkeller, Oct 11 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 18 2011
EXTENSIONS
Wrong formula removed (thanks to Wolfdieter Lang, who pointed this out) by Reinhard Zumkeller, Oct 11 2015
STATUS
approved