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a(1) = 1. a(n) = Sum_{k=1..n-1} floor(n/a(k)).
1

%I #15 Aug 22 2024 04:08:24

%S 1,2,4,7,8,10,12,16,17,20,21,25,26,29,30,35,37,39,40,45,48,50,51,56,

%T 58,61,62,66,68,72,73,78,79,82,85,89,91,93,95,102,103,107,108,111,113,

%U 115,116,123,125,130,133,137,138,140,141,147,148,152,153,160,162,165,168

%N a(1) = 1. a(n) = Sum_{k=1..n-1} floor(n/a(k)).

%H Reinhard Zumkeller, <a href="/A116478/b116478.txt">Table of n, a(n) for n = 1..10000</a>

%F For n >= 2, a(n) also is Sum_{k=1 .. n} b(k), where b(k) is the number of terms of {a(j)} which divide k.

%e a(5)=8 because floor(5/1) + floor(5/2) + floor(5/4) + floor(5/7) = 5 + 2 + 1 + 0 = 8.

%p a[1]:=1: for n from 2 to 70 do a[n]:=sum(floor(n/a[k]),k=1..n-1): od: seq(a[n],n=1..70); # _Emeric Deutsch_, Apr 01 2006

%t s={1};Do[ AppendTo[s,Sum[Floor[n/s[[k]]],{k,n-1}] ] ,{n,2,63}];s (* _James C. McMahon_, Aug 21 2024 *)

%o (Haskell)

%o a116478 n = a116478_list !! (n-1)

%o a116478_list = 1 : f [2..] [1] where

%o f (x:xs) ys = y : f xs (y:ys) where y = sum $ map (div x) ys

%o -- _Reinhard Zumkeller_, Jul 18 2013

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Mar 18 2006

%E More terms from _Emeric Deutsch_, Apr 01 2006