A098464 Numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A098461 A098462 A098463 * A098465 A098466 A098467

Keyword

easy,nonn

Author

T. D. Noe, Sep 09 2004

Status

approved