

A191854


First factor in happy factorization of nth 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
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OFFSET

1,3


COMMENTS

a(n) = A007966(A007969(n)) = A007969(n) / A191855(n);
(a(n), A191855(n)) is a 1happy couple;
notation: B 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}]]; A191854 = Reap[Table[Print[n, " ", f[n]]; If[f[n] != {} && f[n] =!= Null, Sow[f[n][[1]]]], {n, 1, 130}]][[2, 1]] (* JeanFrançois Alcover, Sep 18 2015 *)


PROG

(Haskell)
a191854 = a007966 . a007969  Reinhard Zumkeller, Oct 11 2015


CROSSREFS

Cf. A007966, A007969, A191855.
Sequence in context: A053222 A318762 A262598 * A129646 A277640 A165401
Adjacent sequences: A191851 A191852 A191853 * A191855 A191856 A191857


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



