%I #18 Mar 12 2021 23:47:00
%S 1,6,105,44,63,33,156,20,272,343,38272753,11881,100,66,822,28861,77
%N Least number k such that lcm{1,2,...,k}/denominator of harmonic number H(k) = 2n-1.
%C First occurrence of 2n-1 in A110566.
%C 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
%t 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
%o (Python)
%o from fractions import Fraction
%o from sympy import lcm
%o def A112822(n):
%o k, l, h = 1, 1, Fraction(1,1)
%o while l != h.denominator*(2*n-1):
%o k += 1
%o l = lcm(l,k)
%o h += Fraction(1,k)
%o return k # _Chai Wah Wu_, Mar 06 2021
%Y Cf. A110566, A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821.
%K nonn,more
%O 1,2
%A _Robert G. Wilson v_, Sep 15 2005
%E a(11), a(32) from _Max Alekseyev_, Nov 29 2013
%E a(33)-a(34) from _Chai Wah Wu_, Mar 06 2021
%E a(36), a(38), a(39) from _Chai Wah Wu_, Mar 12 2021