The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002547 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002547

Numerator of the n-th harmonic number H(n) divided by (n+1); a(n) = A001008(n) / ((n+1)*A002805(n)).
(history; published version)

#79 by Charles R Greathouse IV at Sun Feb 16 08:32:26 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#78 by Charles R Greathouse IV at Thu Sep 08 08:44:31 EDT 2022

PROG

(MAGMAMagma) [Numerator(HarmonicNumber(n)/(n+1)): n in [1..35]]; // G. C. Greubel, Jul 03 2019

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#77 by OEIS Server at Fri Jul 12 00:38:24 EDT 2019

LINKS

M. F. Hasler, <a href="/A002547/b002547_1.txt">Table of n, a(n) for n = 1..2000</a> (first 700 terms from Alois P. Heinz)

#76 by Peter Luschny at Fri Jul 12 00:38:24 EDT 2019

STATUS

reviewed

approved

Discussion

Fri Jul 12

00:38

OEIS Server: Installed new b-file as b002547.txt.  Old b-file is now b002547_1.txt.

#75 by Sean A. Irvine at Thu Jul 11 19:20:08 EDT 2019

STATUS

proposed

reviewed

#74 by Peter Luschny at Thu Jul 11 15:31:28 EDT 2019

STATUS

editing

proposed

Discussion

Thu Jul 11

19:19

Sean A. Irvine: New b-file verified, takes my Java 8.8 seconds.

#73 by Peter Luschny at Thu Jul 11 15:31:09 EDT 2019

MAPLE

with(combinat):seq(numer(stirling1(j+1, 2)/(j+1)!*2!*(-1)^(j+1)), j=1..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

#72 by Peter Luschny at Thu Jul 11 15:28:54 EDT 2019

MAPLE

H := proc(a, b) option remember; local m, p, q, r, s;

if b - a <= 1 then return 1, a fi; m := iquo(a + b, 2);

p, q := H(a, m); r, s := H(m, b); p*s + q*r, q*s; end:

A002547 := proc(n) H(1, n+1); numer(%[1]/(%[2]*(n+1))) end:

seq(A002547(n), n=1..30); # Peter Luschny, Jul 11 2019

STATUS

proposed

editing

Discussion

Thu Jul 11

15:30

Peter Luschny: For n = 1..2000 my routine takes 1.5 sec., and interrupted Margolius's routine after 10 minutes.

#71 by Peter Luschny at Thu Jul 11 14:22:56 EDT 2019

STATUS

editing

proposed

#70 by Peter Luschny at Thu Jul 11 14:22:03 EDT 2019

EXAMPLE

a(4) = denominatornumerator(H(4)/(4+1)) = 5.

STATUS

proposed

editing