A022819 a(n) = floor(1/(n-1) + 2/(n-2) + 3/(n-3) + ... + (n-1)/1).

0, 0, 1, 2, 4, 6, 8, 11, 13, 16, 19, 22, 25, 28, 31, 34, 38, 41, 44, 48, 51, 55, 59, 62, 66, 70, 74, 78, 81, 85, 89, 93, 97, 101, 106, 110, 114, 118, 122, 126, 131, 135, 139, 144, 148, 152, 157, 161, 166, 170, 174, 179, 183, 188, 193, 197, 202, 206, 211, 216

Offset

0,4

Comments

a(n) = A214075(n,n-2) for n > 1. - Reinhard Zumkeller, Jul 03 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(sum_{i=2..n} n/i) = floor(A000027(n)*(A001008(n)/A002805(n)-1)) = floor(A006675(n)/A000142(n)) = floor(A001705(n-1)/A000142(n-1)). - Henry Bottomley, May 05 2001

Example

a(2) = floor(1/1) = 1;
a(3) = floor(1/2 + 2/1) = floor(5/2) = 2;
a(4) = floor(1/3 + 2/2 + 3/1) = floor(26/6) = 4.

Mathematica

s=0; Table[s+=HarmonicNumber[j]//N; Floor[s], {j, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2010 *)
Join[{0}, Floor[Accumulate[HarmonicNumber[Range[0, 60]]]]] (* Harvey P. Dale, Sep 16 2019 *)

Prog

(Haskell)
import Data.Ratio ((%))
a022819 n = floor $ sum $ zipWith (%) [1 .. n-1] [n-1, n-2 .. 1]
-- Reinhard Zumkeller, Jul 03 2012

Crossrefs

Cf. A027612.

Sequence in context: A262773 A186152 A004401 * A081527 A070978 A027919

Adjacent sequences: A022816 A022817 A022818 * A022820 A022821 A022822

Keyword

nonn

Author

Clark Kimberling

Status

approved