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A128501 a(n) = lcm{1 <= k <= n, gcd(k, 3) = 1}. 4
1, 1, 2, 2, 4, 20, 20, 140, 280, 280, 280, 3080, 3080, 40040, 40040, 40040, 80080, 1361360, 1361360, 25865840, 25865840, 25865840, 25865840, 594914320, 594914320, 2974571600, 2974571600, 2974571600, 2974571600, 86262576400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Old name was: Denominators of partial sums for a series for Pi/(3*sqrt(3)).

The numerators are given in A128500. See the W. Lang link under A128500.

There appears to be a relationship between a(n) and b(n) = Denominator(3*HarmonicNumber(n)). For n=0..8, b(n)=a(n). For n=9..17, b(n)= 3*a(n). Starting at term 18, b(n)/a(n) = 1, 1, 1/5, 1/5, 1/5, 1/5, 1/5, 1, 1, 9, 9, 9, 9, 9, 9. - Gary Detlefs, Oct 12 2011 [adjusted to new definition by Peter Luschny, Oct 15 2012]

LINKS

Table of n, a(n) for n=0..29.

FORMULA

a(n+1) = denominator(r(n)) with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*S(k,1)/(k+1) with Chebyshev's S-Polynomials S(n,1)=[1,1,0,-1,-1,0] periodic sequence with period 6. See A010892.

MAPLE

A128501 := n -> ilcm(op(select(j->igcd(j, 3) = 1, [$1..n]))):

seq(A128501(i), i=0..28); # Peter Luschny, Oct 15 2012

MATHEMATICA

a[n_] := If[n == 0, 1, LCM @@ Select[Range[n], GCD[#, 3] == 1&]];

Array[a, 30, 0] (* Jean-Fran├žois Alcover, Jun 14 2019, from Maple *)

PROG

(Sage)

def A128501(n): return lcm([j for j in (1..n) if gcd(j, 3) == 1])

[A128501(n) for n in (0..28)]  # Peter Luschny, Oct 15 2012

CROSSREFS

Cf. A003418, A216917, A217858.

Sequence in context: A175185 A257610 A062267 * A288497 A288767 A287745

Adjacent sequences:  A128498 A128499 A128500 * A128502 A128503 A128504

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Apr 04 2007

EXTENSIONS

New name and 1 prepended by Peter Luschny, Oct 15 2012

STATUS

approved

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Last modified April 22 15:23 EDT 2021. Contains 343177 sequences. (Running on oeis4.)