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%I #9 Mar 04 2018 20:53:04
%S 343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,
%T 360
%N Numbers n such that lcm(1,2,3,...,n)/19 equals the denominator of the n-th harmonic number H(n).
%C Positions where 19 occurs in A110566.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>
%t a = h = 1; t = {}; Do[a = LCM[a, n]; h = h + 1/n; If[a/Denominator[h] == 19, AppendTo[t, n]], {n, 10^6}]; t
%t Select[Range[500],Denominator[HarmonicNumber[#]]==LCM@@Range[#]/19&] (* _Harvey P. Dale_, Jan 29 2012 *)
%Y Cf. A002805, A003418, A110566.
%Y Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112822.
%K nonn,more
%O 1,1
%A _Robert G. Wilson v_, Sep 17 2005
%E Definition corrected by _Max Alekseyev_, Mar 03 2007