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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).
5
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
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