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A191855 Second factor in happy factorization of n-th rectangular number. 7
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, 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, 10, 4, 31, 2, 5, 97, 2, 101, 51, 21, 106, 4, 109, 11, 37, 16, 113, 57 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) > 1;

a(n) = A007967(A007969(n)) = A007969(n) / A191854(n);

(A191854(n), a(n)) is a 1-happy couple;

notation: C in the Conway link.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..200

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}]]; A191855 = Reap[Table[Print[n, " ", f[n]];    If[f[n] != {} && f[n] =!= Null, Sow[f[n][[2]]]], {n, 1, 130}]][[2, 1]] (* Jean-Fran├žois Alcover, Sep 18 2015 *)

PROG

(Haskell)

a191855 = a007967 . a007969  -- Reinhard Zumkeller, Oct 11 2015

CROSSREFS

Cf. A007967, A007969, A191854.

Sequence in context: A057337 A163233 A096666 * A064664 A078386 A163254

Adjacent sequences:  A191852 A191853 A191854 * A191856 A191857 A191858

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 18 2011

EXTENSIONS

Wrong formula removed, thanks to Wolfdieter Lang, who pointed this out. Reinhard Zumkeller, Oct 11 2015

STATUS

approved

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Last modified October 16 02:45 EDT 2018. Contains 316252 sequences. (Running on oeis4.)