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A110268
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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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1
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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
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OFFSET
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1,5
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COMMENTS
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a(n) is always an odd prime power, A061345.
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LINKS
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EXAMPLE
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A110566(4) through A110566(10) are {1,1,3,3,3,1,1}, therefore the factors are 1,3,1,1,3,1.
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MATHEMATICA
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f[n_] := LCM @@ Range[n]/Denominator[HarmonicNumber[n]]; Table[ LCM[f[n], f[n + 1]]/GCD[f[n], f[n + 1]], {n, 104}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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