A128500 -id:A128500 - cp's OEIS frontend

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

Offset: 0

Wolfdieter Lang, Apr 04 2007

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]

Cf. A003418, A216917, A217858.

A128501 := n -> ilcm(op(select(j->igcd(j,3) = 1,[$1..n]))):
seq(A128501(i),i=0..28); # Peter Luschny, Oct 15 2012

a[n_] := If[n == 0, 1, LCM @@ Select[Range[n], GCD[#, 3] == 1&]];
Array[a, 30, 0] (* Jean-François Alcover, Jun 14 2019, from Maple *)

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

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.

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

cp's OEIS Frontend

A128501 a(n) = lcm{1 <= k <= n, gcd(k, 3) = 1}.

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