

A191855


Second factor in happy factorization of nth 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
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OFFSET

1,1


COMMENTS

a(n) > 1;
a(n) = A007967(A007969(n)) = A007969(n) / A191854(n);
(A191854(n), a(n)) is a 1happy 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]] (* JeanFrançois 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 A323637 A349637
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) by Reinhard Zumkeller, Oct 11 2015


STATUS

approved



