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A051417 Quotients of consecutive values of lcm {1, 3, 5 ..., 2n-1} or A025547(n+1)/A025547(n).

%I A051417 #30 Jul 03 2025 01:02:42
%S A051417 3,5,7,3,11,13,1,17,19,1,23,5,3,29,31,1,1,37,1,41,43,1,47,7,1,53,1,1,
%T A051417 59,61,1,1,67,1,71,73,1,1,79,3,83,1,1,89,1,1,1,97,1,101,103,1,107,109,
%U A051417 1,113,1,1,1,11,1,5,127,1,131,1,1,137,139,1,1,1,1,149,151,1,1,157,1,1
%N A051417 Quotients of consecutive values of lcm {1, 3, 5 ..., 2n-1} or A025547(n+1)/A025547(n).
%C A051417 a(n) = GCD( C(2n+1,1),C(2n+2,2),...,C(3n,n) ) where C(n,k)=binomial(n,k). - _Benoit Cloitre_, Jan 31 2003
%C A051417 a(n) = greatest common divisor of entries of zigzag matrix Z(n), as defined in A088961. - _Reinhard Zumkeller_, Oct 25 2013
%H A051417 Reinhard Zumkeller, <a href="/A051417/b051417.txt">Table of n, a(n) for n = 1..1000</a>
%H A051417 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A051417 a(n) = cyclotomic(2*n+1, 1). - _Vladeta Jovovic_, Apr 05 2004
%F A051417 a(n) = A014963(2*n+1). - _Ridouane Oudra_, Jul 02 2025
%e A051417 a(5) = A025547(6)/A025547(5) = 3465/315 = 11.
%t A051417 Table[Cyclotomic[2n+1,1],{n,90}]  (* _Harvey P. Dale_, Apr 02 2011 *)
%t A051417 #[[2]]/#[[1]]&/@Partition[Table[LCM@@Range[1,2n+1,2],{n,0,80}],2,1] (* _Harvey P. Dale_, Mar 04 2013 *)
%o A051417 (Haskell)
%o A051417 a051417 n = a051417_list !! (n-1)
%o A051417 a051417_list = zipWith div (tail a025547_list) a025547_list
%o A051417 -- _Reinhard Zumkeller_, Oct 25 2013
%Y A051417 Cf. A020500, A025547, A014963.
%K A051417 easy,nice,nonn
%O A051417 1,1
%A A051417 _Asher Auel_
%E A051417 More terms from _James Sellers_