A124056 a(1)=1. a(n) = number of terms from among the first (n-1) terms of the sequence which divide a(n-1).

1, 1, 2, 3, 3, 4, 4, 5, 3, 5, 4, 6, 7, 3, 6, 9, 7, 4, 7, 5, 5, 6, 10, 8, 8, 9, 8, 10, 9, 9, 10, 10, 11, 3, 7, 6, 12, 17, 3, 8, 11, 4, 8, 13, 3, 9, 14, 8, 14, 9, 15, 14, 10, 12, 21, 14, 11, 5, 7, 7, 8, 15, 16, 16, 17, 4, 9, 16, 19, 3, 10, 14, 14, 15, 18, 23, 3, 11, 6, 17, 5, 8, 17, 6, 18, 27, 19

Offset: 1

Author

Leroy Quet, Nov 03 2006

Keywords

• nonn

Comments

First occurrence of k: 1, 3, 4, 6, 8, 12, 13, 24, 16, 23, 33, 37, 44, 47, 51, 63, 38, 75, 69, 101, 55, 91, 76, 132, 102, ..., . - Robert G. Wilson v, Nov 05 2006

a(n+1) = number of preceding terms that are divisors of a(n); a(1) = 1. - Reinhard Zumkeller, May 23 2013

Examples

			a(12) is 6. a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=3, a(9)=3 and a(12)=6 are the seven terms that divide 6. So a(13)= 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027750.

Cf. A088167 (counting divisors of n instead of those of a(n)).

Programs

Haskell

import Data.List (isInfixOf)
a124056 n = a124056_list !! (n-1)
a124056_list = 1 : f [1] where
   f xs@(x:_) = y : f (y : xs) where
     y = length $ filter (flip elem $ a027750_row x) xs
-- Reinhard Zumkeller, May 23 2013

Mathematica

f[s_] := Append[s, Count[Mod[s[[ -1]], s], 0]]; Nest[f, {1, 1}, 86] (* Robert G. Wilson v *)
a[1]= 1; L[1]= {1}; a[n_]:=a[n]= Sum[If[Mod[a[n - 1], L[n - 1][[i]]]==0, 1, 0], {i,1,n-1}]; L[n_]:=L[n]= Table[a[i], {i, 1, n}]; L[87] (* Joel B. Lewis, Nov 05 2006 *)

Extensions

More terms from Robert G. Wilson v and Joel B. Lewis, Nov 05 2006