A106530 Least common multiple of all parts in Zeckendorf representation of n.

1, 2, 3, 3, 5, 5, 10, 8, 8, 8, 24, 24, 13, 13, 26, 39, 39, 65, 65, 130, 21, 21, 42, 21, 21, 105, 105, 210, 168, 168, 168, 168, 168, 34, 34, 34, 102, 102, 170, 170, 170, 136, 136, 136, 408, 408, 442, 442, 442, 1326, 1326, 2210, 2210, 2210, 55, 55, 110, 165, 165, 55, 55, 110, 440, 440

Offset: 1

Author

Reinhard Zumkeller, May 08 2005

Keywords

• nonn
• look

Comments

Records: A106531(n) = a(A106532(n)).

a(n) = lcm_{k=0..A007895(n)-1} A035516(n,k). - Reinhard Zumkeller, Mar 10 2013

Examples

			n=33: 21+8+3+1 = 33 -> a(33) = lcm(21,8,3,1) = (21*8*3*1)/3 = 168.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16384 (first 10000 terms from Reinhard Zumkeller)
• Eric Weisstein's World of Mathematics, Zeckendorf Representation
• Index entries for sequences related to lcm's.

Crossrefs

Cf. A000045, A014417, A003714.

Programs

Haskell

a106530 = foldr lcm 1 . a035516_row -- Reinhard Zumkeller, Mar 10 2013

Maple

F:= combinat[fibonacci]:
a:= proc(n) option remember; local j;
      if n=0 then 1
    else for j from 2 while F(j+1)<=n do od;
         ilcm(a(n-F(j)), F(j))
      fi
    end:
seq(a(n), n=1..64);  # Alois P. Heinz, Mar 17 2018

Mathematica

t = Fibonacci /@ Range@ 21; Table[LCM @@ If[MemberQ[t, n], {n}, Most@ MapAt[# + 1 &, Abs@ Differences@ FixedPointList[# - First@ Reverse@ TakeWhile[t, Function[k, # >= k]] &, n], -1]], {n, 61}] (* Michael De Vlieger, May 17 2016 *)