A116478 a(1) = 1. a(n) = Sum_{k=1..n-1} floor(n/a(k)).

1, 2, 4, 7, 8, 10, 12, 16, 17, 20, 21, 25, 26, 29, 30, 35, 37, 39, 40, 45, 48, 50, 51, 56, 58, 61, 62, 66, 68, 72, 73, 78, 79, 82, 85, 89, 91, 93, 95, 102, 103, 107, 108, 111, 113, 115, 116, 123, 125, 130, 133, 137, 138, 140, 141, 147, 148, 152, 153, 160, 162, 165, 168

Offset

1,2

Links

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

Formula

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.

Example

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

Maple

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

Prog

(Haskell)
a116478 n = a116478_list !! (n-1)
a116478_list = 1 : f [2..] [1] where
   f (x:xs) ys = y : f xs (y:ys) where y = sum $ map (div x) ys
-- Reinhard Zumkeller, Jul 18 2013

Crossrefs

Sequence in context: A131346 A341350 A047540 * A207829 A207827 A047236

Adjacent sequences: A116475 A116476 A116477 * A116479 A116480 A116481

Keyword

easy,nonn

Author

Leroy Quet, Mar 18 2006

Extensions

More terms from Emeric Deutsch, Apr 01 2006

Status

approved