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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).
18
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, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149
OFFSET
1,2
COMMENTS
Numbers k such that A110566(k) = 1.
Shiu (2016) conjectured that this sequence is infinite. - Amiram Eldar, Feb 02 2021
LINKS
Peter Shiu, The denominators of harmonic numbers, arXiv:1607.02863 [math.NT], 2016.
Eric Weisstein's World of Mathematics, Harmonic Number.
MATHEMATICA
Select[Range[250], LCM@@Range[ # ]==Denominator[HarmonicNumber[ # ]]&]
PROG
(PARI) isok(n) = lcm(vector(n, i, i)) == denominator(sum(i=1, n, 1/i)); \\ Michel Marcus, Mar 07 2018
(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
CROSSREFS
Cf. A002805 (denominator of H(n)), A003418 (lcm(1, 2, ..., n)), A110566.
Sequence in context: A265335 A179223 A069117 * A068586 A068585 A037472
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Sep 09 2004
STATUS
approved