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A025547 Least common multiple of {1,3,5,...,2n-1}.

%I A025547 #52 Feb 16 2025 08:32:35
%S A025547 1,3,15,105,315,3465,45045,45045,765765,14549535,14549535,334639305,
%T A025547 1673196525,5019589575,145568097675,4512611027925,4512611027925,
%U A025547 4512611027925,166966608033225,166966608033225,6845630929362225,294362129962575675,294362129962575675
%N A025547 Least common multiple of {1,3,5,...,2n-1}.
%C A025547 This sequence coincides with the sequence f(n) = denominator of 1 + 1/3 + 1/5 + 1/7 + ... + 1/(2n-1) iff n <= 38. But a(39) = 6414924694381721303722858446525, f(39) = 583174972216520118520259858775. - _T. D. Noe_, Aug 04 2004 [See A350670(n-1).]
%C A025547 Coincides for n=1..42 with the denominators of a series for Pi*sqrt(2)/4 and then starts to differ. See A127676.
%C A025547 a(floor((n+1)/2)) = gcd(a(n), A051426(n)). - _Reinhard Zumkeller_, Apr 25 2011
%C A025547 A051417(n) = a(n+1)/a(n).
%H A025547 T. D. Noe, <a href="/A025547/b025547.txt">Table of n, a(n) for n = 1..200</a>
%H A025547 Yue-Wu Li and Feng Qi, <a href="https://doi.org/10.3390/axioms13050317">A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments</a>, Axioms (2024) Vol. 13, Art. No. 317. See p. 11 of 24.
%H A025547 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JeepProblem.html">Jeep Problem</a>, <a href="https://mathworld.wolfram.com/Pi.html">Pi</a>, <a href="https://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>, <a href="https://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a>
%H A025547 Wikipedia, <a href="http://en.wikipedia.org/wiki/Least_common_multiple">Least common multiple</a>
%H A025547 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%p A025547 A025547:=proc(n) local i,t1; t1:=1; for i from 1 to n do t1:=lcm(t1,2*i-1); od: t1; end;
%p A025547 f := n->denom(add(1/(2*k-1),k=0..n)); # a different sequence!
%t A025547 a = 1; Join[{1}, Table[a = LCM[a, n], {n, 3, 125, 2}]] (* _Zak Seidov_, Jan 18 2011 *)
%t A025547 nn=30;With[{c=Range[1,2*nn,2]},Table[LCM@@Take[c,n],{n,nn}]] (* _Harvey P. Dale_, Jan 27 2013 *)
%o A025547 (Haskell)
%o A025547 a025547 n = a025547_list !! (n-1)
%o A025547 a025547_list = scanl1 lcm a005408_list
%o A025547 -- _Reinhard Zumkeller_, Oct 25 2013, Apr 25 2011
%o A025547 (PARI) a(n)=lcm(vector(n,k,2*k-1)) \\ _Charles R Greathouse IV_, Nov 20 2012
%o A025547 (Python) # generates initial segment of sequence
%o A025547 from math import gcd
%o A025547 from itertools import accumulate
%o A025547 def lcm(a, b): return a * b // gcd(a, b)
%o A025547 def aupton(nn): return list(accumulate((2*i+1 for i in range(nn)), lcm))
%o A025547 print(aupton(23)) # _Michael S. Branicky_, Mar 28 2022
%Y A025547 Cf. A007509, A025550, A075135. The numerators are in A074599.
%Y A025547 Cf. A003418 (LCM of {1..n}).
%Y A025547 Cf. A005408, A350670.
%K A025547 easy,nice,nonn
%O A025547 1,2
%A A025547 _Clark Kimberling_