A121369 a(1) = a(2) = 1, a(n) = A007947(a(n-1)) + A007947(a(n-2)) for n >= 3, i.e., a(n) is the largest squarefree divisor of a(n-1) plus the largest squarefree divisor of a(n-2).

1, 1, 2, 3, 5, 8, 7, 9, 10, 13, 23, 36, 29, 35, 64, 37, 39, 76, 77, 115, 192, 121, 17, 28, 31, 45, 46, 61, 107, 168, 149, 191, 340, 361, 189, 40, 31, 41, 72, 47, 53, 100, 63, 31, 52, 57, 83, 140, 153, 121, 62, 73, 135, 88, 37, 59, 96, 65, 71, 136, 105, 139, 244, 261, 209, 296

Offset: 1

Author

Leroy Quet, Jul 23 2006

Keywords

• nonn

Comments

First terms occurring more than once: 1, 31, 37, 121, ...: a(25)=a(37)=a(44)=31, a(16)=a(55)=37, a(22)=a(50)=121. - Reinhard Zumkeller, May 05 2013

Examples

			6 is the largest squarefree divisor of a(12) = 36. 29 is the largest squarefree divisor of a(13) = 29. So a(14) = 6 + 29 = 35.
		

Links

• Reinhard Zumkeller and Michael De Vlieger, Table of n, a(n) for n = 1..1000 (first 250 terms from Reinhard Zumkeller).

Crossrefs

Cf. A007947, A121367, A121368.

Cf. A000045.

Programs

Haskell

import Data.Function (on)
a121369 n = a121369_list !! (n-1)
a121369_list = 1 : 1 : zipWith ((+) `on` a007947)
                       a121369_list (tail a121369_list)
-- Reinhard Zumkeller, May 05 2013

Maple

with(numtheory): A007947:= proc(n) local i, t1, t2; t1 := ifactors(n)[2]; t2 := mul(t1[i][1], i=1..nops(t1)); end: a:=proc(n) if n=1 or n=2 then 1 else A007947(a(n-1))+A007947(a(n-2)) fi end: seq(a(n),n=1..20); # Emeric Deutsch, Jul 24 2006

Mathematica

Nest[Append[#, Total@ Map[SelectFirst[Reverse@ Divisors@ #, SquareFreeQ] &, Take[#, -2]]] &, {1, 1}, 64] (* Michael De Vlieger, Oct 10 2017 *)

Extensions

More terms from Emeric Deutsch, Jul 24 2006

More terms from R. J. Mathar, May 18 2007