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 A110566 a(n) = lcm{1,2,...,n}/denominator of harmonic number H(n). 23
 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 15, 45, 45, 45, 15, 3, 3, 1, 1, 1, 1, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 77, 77, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 27, 27, 27, 9, 9, 9, 3, 3, 3, 3, 3, 33, 33, 33, 33, 11, 11, 11, 11, 11, 11, 11, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) is always odd. Unsorted union: 1, 3, 15, 45, 11, 77, 7, 9, 27, 33, 25, 5, 55, 275, 13, 39, 17, 49, 931, 19, 319, 75, ..., . See A112810. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A003418(n)/A002805(n) = A025529(n)/A001008(n). From Franz Vrabec, Sep 21 2005: (Start) a(n) = gcd(lcm{1,2,...,n}, H(n)*lcm{1,2,...,n}). a(n) = gcd(A003418(n), A025529(n)). (End) EXAMPLE a(6) = 60/20 = 3 because lcm{1,2,3,4,5,6}=60 and H(6)=49/20. MAPLE H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end: L:= proc(n) L(n):= ilcm(n, `if`(n=1, 1, L(n-1))) end: a:= n-> L(n)/denom(H(n)): seq(a(n), n=1..100);  # Alois P. Heinz, Aug 30 2012 MATHEMATICA f[n_] := LCM @@ Range[n]/Denominator[HarmonicNumber[n]]; Table[ f[n], {n, 90}] (* Robert G. Wilson v *) PROG (PARI) a(n) = lcm(vector(n, k, k))/denominator(sum(k=1, n, 1/k)); \\ Michel Marcus, Mar 07 2018 (Python) from sympy import lcm, harmonic def A110566(n): return lcm([k for k in range(1, n+1)])//harmonic(n).q # Chai Wah Wu, Mar 06 2021 CROSSREFS Cf. A001008, A002805, A003418, A025529, A098464, A112810, A112822. Sequence in context: A019801 A086634 A066601 * A126066 A177693 A131289 Adjacent sequences:  A110563 A110564 A110565 * A110567 A110568 A110569 KEYWORD nonn AUTHOR Franz Vrabec, Sep 12 2005 EXTENSIONS More terms from Robert G. Wilson v, Sep 15 2005 STATUS approved

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Last modified July 29 05:59 EDT 2021. Contains 346340 sequences. (Running on oeis4.)