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A110268 Consider the sequence A110566: lcm{1,2,...,n}/denominator of harmonic number H(n). a(n) is the factor that is changed going from A110566(n) to A110566(n+1). 1

%I

%S 1,1,1,1,3,1,1,3,1,1,1,1,1,1,1,1,3,1,5,3,1,1,3,5,1,3,1,1,1,1,1,11,1,1,

%T 1,1,1,1,1,1,7,1,11,1,1,1,1,7,1,1,1,1,3,1,1,1,1,1,1,1,1,3,1,1,3,1,1,3,

%U 1,1,3,1,1,1,1,11,1,1,1,3,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,25,1,1,1,1,5

%N Consider the sequence A110566: lcm{1,2,...,n}/denominator of harmonic number H(n). a(n) is the factor that is changed going from A110566(n) to A110566(n+1).

%C a(n) is always an odd prime power, A061345.

%e A110566(4) through A110566(10) are {1,1,3,3,3,1,1}, therefore the factors are 1,3,1,1,3,1.

%t f[n_] := LCM @@ Range[n]/Denominator[HarmonicNumber[n]]; Table[ LCM[f[n], f[n + 1]]/GCD[f[n], f[n + 1]], {n, 104}]

%o (PARI) f(n) = lcm(vector(n, k, k))/denominator(sum(k=1, n, 1/k));

%o a(n) = my(x = f(n+1)/f(n)); if (x > 1, x, 1/x); \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A110566, A112811.

%K nonn

%O 1,5

%A _Robert G. Wilson v_, Sep 17 2005

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)