A007966 First factor in happy factorization of n.

0, 1, 1, 1, 2, 1, 2, 7, 2, 3, 1, 1, 3, 1, 7, 3, 4, 1, 2, 1, 4, 3, 2, 23, 4, 5, 1, 1, 7, 1, 5, 31, 16, 11, 17, 5, 6, 1, 2, 3, 2, 1, 6, 1, 11, 5, 23, 47, 6, 7, 1, 1, 4, 1, 2, 11, 7, 3, 1, 1, 15, 1, 31, 7, 8, 1, 2, 1, 4, 23, 5, 71, 8, 1, 1, 25, 19, 7, 26, 79, 8, 9, 1, 1, 3, 1, 2, 3, 4, 1, 9

Offset

0,5

Comments

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

a(A007969(n)) = A191854(n); a(A007970(n)) = A191856(n). - Reinhard Zumkeller, Jun 18 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..300

J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.

Initial Happy Factorization Data

Mathematica

r[b_, c_, d_] := (red = Reduce[x > 0 && y > 0 && b*x^2 + d == c*y^2, {x, y}, Integers] /. C[1] -> 1 // Simplify; If[Head[red] === Or, red[[1]], red]); f[n_] := f[n] = If[IntegerQ[rn = Sqrt[n]], {0, rn, rn, rn, rn}, Catch[Do[b = bc[[1]]; c = bc[[2]]; If[ c > 1 && (r0 = r[b, c, 1]) =!= False, rr = ToRules[r0]; x0 = x /. rr; y0 = y /. rr; Throw[{1, b, c, x0, y0}]]; If[ b > 1 && (r0 = r[c, b, 1]) =!= False, rr = ToRules[r0]; x0 = x /. rr; y0 = y /. rr; Throw[{1, c, b, x0, y0}]]; If[ (r0 = r[b, c, 2]) =!= False, rr = ToRules[r0]; x0 = x /. rr; y0 = y /. rr; If[OddQ[x0] && OddQ[y0], Throw[{2, b, c, x0, y0}]]]; If[ (r0 = r[c, b, 2]) =!= False, rr = ToRules[r0]; x0 = x /. rr; y0 = y /. rr; If[OddQ[x0] && OddQ[y0], Throw[{2, c, b, x0, y0}]]]; , {bc, Union[Sort[{#, n/#}] & /@ Divisors[n]]} ]]]; a[n_] := f[n][[2]]; A007966 = Table[Print[a[n]]; a[n], {n, 0, 90}] (* Jean-François Alcover, Jun 25 2012 *)

Prog

(Haskell)
import Data.List (genericIndex)
a007966 n = genericIndex a007966_list n
a007966_list = map fst hCouples
-- Pairs hCouples are defined in A007968.
-- Reinhard Zumkeller, Oct 11 2015

Crossrefs

Cf. A191914.

Cf. A007968, A007969, A007970, A191854, A191856.

Sequence in context: A131057 A051852 A054495 * A224609 A278710 A011241

Adjacent sequences: A007963 A007964 A007965 * A007967 A007968 A007969

Keyword

nonn

Author

J. H. Conway

Status

approved