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A128501 a(n) = lcm{1 <= k <= n, gcd(k, 3) = 1}. 4

%I

%S 1,1,2,2,4,20,20,140,280,280,280,3080,3080,40040,40040,40040,80080,

%T 1361360,1361360,25865840,25865840,25865840,25865840,594914320,

%U 594914320,2974571600,2974571600,2974571600,2974571600,86262576400

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

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

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

%C 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]

%F 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.

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

%p seq(A128501(i),i=0..28); # _Peter Luschny_, Oct 15 2012

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

%t Array[a, 30, 0] (* _Jean-Fran├žois Alcover_, Jun 14 2019, from Maple *)

%o (Sage)

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

%o [A128501(n) for n in (0..28)] # _Peter Luschny_, Oct 15 2012

%Y Cf. A003418, A216917, A217858.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Apr 04 2007

%E New name and 1 prepended by _Peter Luschny_, Oct 15 2012

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Last modified May 9 07:55 EDT 2021. Contains 343692 sequences. (Running on oeis4.)