A112822 - OEIS

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

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OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..17.

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

PROG

(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

CROSSREFS