A128438 a(n) = floor((denominator of H(n))/n), where H(n) = Sum_{k=1..n} 1/k, the n-th harmonic number.

1, 1, 2, 3, 12, 3, 20, 35, 280, 252, 2520, 2310, 27720, 25740, 24024, 45045, 720720, 226893, 4084080, 775975, 246341, 235144, 5173168, 14872858, 356948592, 343219800, 2974571600, 2868336900, 80313433200, 77636318760, 2329089562800

Offset: 1

Author

Leroy Quet, Mar 03 2007

Keywords

• nonn

Comments

This is very similar to A027611, which is a different sequence. - N. J. A. Sloane, Nov 21 2008

Indices where a(n) differs from A027611 are terms of A074791. - Gary Detlefs, Sep 03 2011

Examples

			The sequence denominator(H(n))/n begins 1, 1, 2, 3, 12, 10/3, 20, 35, 280, 252, 2520, 2310, ..., so the present sequence begins 1, 1, 2, 3, 12, 3, 20, 35, 280, 252, 2520, 2310, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2310

Crossrefs

Cf. A128437, A002805, A027611, A074791.

Programs

Maple

H:=n->sum(1/k,k=1..n): a:=n->floor(denom(H(n))/n): seq(a(n),n=1..34); # Emeric Deutsch, Mar 25 2007

Mathematica

seq = {}; s = 0; Do[s += 1/n; AppendTo[seq, Floor[Denominator[s]/n]], {n, 1, 30}]; seq (* Amiram Eldar, Sep 18 2021 *)
Table[Floor[Denominator[HarmonicNumber[n]]/n],{n,40}] (* Harvey P. Dale, Nov 24 2023 *)

Python

from sympy import harmonic
def A128438(n): return harmonic(n).q//n # Chai Wah Wu, Sep 27 2021

Extensions

More terms from Emeric Deutsch, Mar 25 2007