A112811 -id:A112811 - cp's OEIS frontend

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

Robert G. Wilson v, Sep 17 2005

nonn

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

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

Cf. A110566, A112811.

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

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

A112812 a(n) is length of n-th run in A110566.

Original entry on oeis.org

5, 3, 9, 2, 1, 3, 1, 2, 6, 9, 2, 5, 5, 9, 3, 3, 3, 5, 4, 7, 12, 5, 5, 10, 1, 4, 31, 6, 7, 20, 9, 9, 9, 27, 29, 17, 5, 7, 35, 6, 1, 18, 2, 14, 29, 29, 29, 20, 2, 14, 6, 19, 4, 30, 8, 27, 6, 2, 8, 11, 4, 4, 19, 18, 5, 14, 18, 26, 11, 72, 10, 19, 6, 11, 22, 11, 33, 6, 5, 22, 4, 7, 99, 97, 2, 44, 9

Offset: 1

Robert G. Wilson v, Sep 20 2005

nonn

Cf. A110566, A112811.

f[n_] := LCM @@ Range[n]/Denominator[HarmonicNumber[n]]; Length /@ Split[Table[f[n], {n, 1220}]]

Edited by Don Reble, Nov 08 2005

Definition clarified by Omar E. Pol, Dec 26 2008

cp's OEIS Frontend

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).

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