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

1,3

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A007947, A121367, A121368.

Cf. A000045.

Sequence in context: A271621 A116917 A354184 * A284172 A230445 A125727

Adjacent sequences: A121366 A121367 A121368 * A121370 A121371 A121372

Keyword

nonn

Author

Leroy Quet, Jul 23 2006

Extensions

More terms from Emeric Deutsch, Jul 24 2006

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

Status

approved