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%I #21 Sep 22 2015 12:28:59
%S 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,
%T 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,
%U 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
%N a(1)=1. a(n) = number of terms from among the first (n-1) terms of the sequence which divide a(n-1).
%C 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
%C a(n+1) = number of preceding terms that are divisors of a(n); a(1) = 1. - _Reinhard Zumkeller_, May 23 2013
%H Reinhard Zumkeller, <a href="/A124056/b124056.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t f[s_] := Append[s, Count[Mod[s[[ -1]], s], 0]]; Nest[f, {1, 1}, 86] (* _Robert G. Wilson v_ *)
%t 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[40] (_Joel B. Lewis_, Nov 05 2006)
%o (Haskell)
%o import Data.List (isInfixOf)
%o a124056 n = a124056_list !! (n-1)
%o a124056_list = 1 : f [1] where
%o f xs@(x:_) = y : f (y : xs) where
%o y = length $ filter (flip elem $ a027750_row x) xs
%o -- _Reinhard Zumkeller_, May 23 2013
%Y Cf. A027750.
%Y Cf. A088167 (counting divisors of n instead of those of a(n)).
%K nonn
%O 1,3
%A _Leroy Quet_, Nov 03 2006
%E More terms from _Robert G. Wilson v_ and _Joel B. Lewis_, Nov 05 2006
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