The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A098464 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A098464

Numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k).
(history; published version)

#26 by Joerg Arndt at Mon Mar 08 02:09:16 EST 2021

STATUS

reviewed

approved

#25 by Michel Marcus at Mon Mar 08 02:04:36 EST 2021

STATUS

proposed

reviewed

#24 by Chai Wah Wu at Mon Mar 08 01:03:40 EST 2021

STATUS

editing

proposed

#23 by Chai Wah Wu at Sun Mar 07 23:44:12 EST 2021

PROG

h += Fraction(1, k) # Chai Wah Wu, Mar 07 2021

#22 by Chai Wah Wu at Sun Mar 07 23:44:01 EST 2021

PROG

(Python)

from fractions import Fraction

from sympy import lcm

k, l, h, A098464_list = 1, 1, Fraction(1, 1), []

while k < 10**6:

if l == h.denominator:

A098464_list.append(k)

k += 1

l = lcm(l, k)

h += Fraction(1, k) # Chai Wah Wu, Mar 07 2021

STATUS

approved

editing

#21 by Michel Marcus at Tue Feb 02 04:33:25 EST 2021

STATUS

reviewed

approved

#20 by Joerg Arndt at Tue Feb 02 03:45:29 EST 2021

STATUS

proposed

reviewed

#19 by Amiram Eldar at Tue Feb 02 02:19:02 EST 2021

STATUS

editing

proposed

#18 by Amiram Eldar at Tue Feb 02 02:15:28 EST 2021

COMMENTS

Numbers k such that A110566(k) = 1.

Shiu (2016) conjectured that this sequence is infinite. - Amiram Eldar, Feb 02 2021

LINKS

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

CROSSREFS

Cf. A002805 (denominator of H(n)), A003418 (lcm(1, 2, ..., n)), A110566.

#17 by Amiram Eldar at Tue Feb 02 02:14:47 EST 2021

LINKS

Peter Shiu, <a href="https://arxiv.org/abs/1607.02863">The denominators of harmonic numbers</a>, arXiv:1607.02863 [math.NT], 2016.