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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.)