%I #26 Mar 08 2021 02:09:16

%S 1,2,3,4,5,9,10,11,12,13,14,15,16,17,27,28,29,30,31,32,49,50,51,52,53,

%T 88,89,90,91,92,93,94,95,96,97,98,99,125,126,127,128,129,130,131,132,

%U 133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149

%N Numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k).

%C Numbers k such that A110566(k) = 1.

%C Shiu (2016) conjectured that this sequence is infinite. - _Amiram Eldar_, Feb 02 2021

%H Amiram Eldar, <a href="/A098464/b098464.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t Select[Range[250], LCM@@Range[ # ]==Denominator[HarmonicNumber[ # ]]&]

%o (PARI) isok(n) = lcm(vector(n, i, i)) == denominator(sum(i=1, n, 1/i)); \\ _Michel Marcus_, Mar 07 2018

%o (Python)

%o from fractions import Fraction

%o from sympy import lcm

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

%o while k < 10**6:

%o if l == h.denominator:

%o A098464_list.append(k)

%o k += 1

%o l = lcm(l,k)

%o h += Fraction(1,k) # _Chai Wah Wu_, Mar 07 2021

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

%K easy,nonn

%O 1,2

%A _T. D. Noe_, Sep 09 2004