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A007967 Second factor in happy factorization of n. 8
0, 1, 2, 3, 2, 5, 3, 1, 4, 3, 10, 11, 4, 13, 2, 5, 4, 17, 9, 19, 5, 7, 11, 1, 6, 5, 26, 27, 4, 29, 6, 1, 2, 3, 2, 7, 6, 37, 19, 13, 20, 41, 7, 43, 4, 9, 2, 1, 8, 7, 50, 51, 13, 53, 27, 5, 8, 19, 58, 59, 4, 61, 2, 9, 8, 65, 33, 67, 17, 3, 14, 1, 9, 73, 74, 3, 4, 11, 3, 1, 10, 9, 82, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = n / A007966(n);

a(A007969(n)) = A191855(n); a(A007970(n)) = A191857(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][[3]]; A007967 = Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 90}] (* Jean-Fran├žois Alcover, Sep 18 2015 *)

PROG

(Haskell)

import Data.List (genericIndex)

a007967 n = genericIndex a007967_list n

a007967_list = map snd hCouples

-- Pairs hCouples are defined in A007968.

-- Reinhard Zumkeller, Oct 11 2015

CROSSREFS

Cf. A191914.

Cf. A007968, A007969, A007970, A191855, A191857.

Sequence in context: A103309 A248207 A174621 * A054494 A112764 A108728

Adjacent sequences:  A007964 A007965 A007966 * A007968 A007969 A007970

KEYWORD

nonn,easy,nice

AUTHOR

J. H. Conway

STATUS

approved

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Last modified October 20 01:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)