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A110566 a(n) = lcm{1,2,...,n}/denominator of harmonic number H(n). 20
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.

Also gcd(lcm{1,2,...,n}, H(n)*lcm{1,2,...,n}). - Franz Vrabec, Sep 21 2005

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A003418(n)/A002805(n) = A025529(n)/A001008(n).

a(n) = gcd(A003418(n), A025529(n)). - Franz Vrabec, Sep 21 2005

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

CROSSREFS

Cf. A001008, A002805, A003418, A025529, A098464, 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 22 20:51 EDT 2019. Contains 325226 sequences. (Running on oeis4.)