A112822 Least number k such that lcm{1,2,...,k}/denominator of harmonic number H(k) = 2n-1.

1, 6, 105, 44, 63, 33, 156, 20, 272, 343, 38272753, 11881, 100, 66, 822, 28861, 77

Offset: 1

Author

Robert G. Wilson v, Sep 15 2005

Keywords

• nonn
• more

Comments

First occurrence of 2n-1 in A110566.

Sequence continues: a(18)=?, 1332, 162, 2758521, 24649, 21, a(24)=?, 294, a(26)=?, 1166, 110, 126059, 201957, 3660, 37553041, 344929, 296341, a(35)=?, 25155299, a(37)=?, 500, 42

Crossrefs

Cf. A110566, A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821.

Programs

Mathematica

a = h = 1; t = Table[0, {100}]; Do[a = LCM[a, n]; h = h + 1/n; b = a/Denominator[h]; If[b < 101 && t[[(b + 1)/2]] == 0, t[[(b + 1)/2]] = n], {n, 500000}]; t

Python

from fractions import Fraction
from sympy import lcm
def A112822(n):
    k, l, h = 1, 1, Fraction(1,1)
    while l != h.denominator*(2*n-1):
        k += 1
        l = lcm(l,k)
        h += Fraction(1,k)
    return k # Chai Wah Wu, Mar 06 2021

Extensions

a(11), a(32) from Max Alekseyev, Nov 29 2013

a(33)-a(34) from Chai Wah Wu, Mar 06 2021

a(36), a(38), a(39) from Chai Wah Wu, Mar 12 2021