A128438 - OEIS

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

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OFFSET

1,3

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

LINKS

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

EXAMPLE

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, ...

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 *)

PROG

(Python)

from sympy import harmonic

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

CROSSREFS

Cf. A128437, A002805, A027611, A074791.

Sequence in context: A140970 A058523 A103782 * A286202 A286413 A288201

Adjacent sequences: A128435 A128436 A128437 * A128439 A128440 A128441

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 03 2007

EXTENSIONS

More terms from Emeric Deutsch, Mar 25 2007

STATUS

approved