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, 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, 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, 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

Offset: 1

Author

Robert G. Wilson v, Sep 17 2005

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A110566, A112811.

Programs

Mathematica

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

PARI

f(n) = lcm(vector(n, k, k))/denominator(sum(k=1, n, 1/k));
a(n) = my(x = f(n+1)/f(n)); if (x > 1, x, 1/x); \\ Michel Marcus, Mar 07 2018