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

1, 3, 15, 105, 315, 3465, 45045, 45045, 765765, 14549535, 14549535, 334639305, 1673196525, 5019589575, 145568097675, 4512611027925, 4512611027925, 4512611027925, 166966608033225, 166966608033225, 6845630929362225, 294362129962575675, 294362129962575675

Offset

1,2

Comments

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).]

Coincides for n=1..42 with the denominators of a series for Pi*sqrt(2)/4 and then starts to differ. See A127676.

a(floor((n+1)/2)) = gcd(a(n), A051426(n)). - Reinhard Zumkeller, Apr 25 2011

A051417(n) = a(n+1)/a(n).

Links

T. D. Noe, Table of n, a(n) for n = 1..200

Yue-Wu Li and Feng Qi, A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments, Axioms (2024) Vol. 13, Art. No. 317. See p. 11 of 24.

Eric Weisstein's World of Mathematics, Jeep Problem, Pi, Pi Continued Fraction, Least Common Multiple

Wikipedia, Least common multiple

Index entries for sequences related to lcm's

Maple

A025547:=proc(n) local i, t1; t1:=1; for i from 1 to n do t1:=lcm(t1, 2*i-1); od: t1; end;
f := n->denom(add(1/(2*k-1), k=0..n)); # a different sequence!

Mathematica

a = 1; Join[{1}, Table[a = LCM[a, n], {n, 3, 125, 2}]] (* Zak Seidov, Jan 18 2011 *)
nn=30; With[{c=Range[1, 2*nn, 2]}, Table[LCM@@Take[c, n], {n, nn}]] (* Harvey P. Dale, Jan 27 2013 *)

Prog

(Haskell)
a025547 n = a025547_list !! (n-1)
a025547_list = scanl1 lcm a005408_list
-- Reinhard Zumkeller, Oct 25 2013, Apr 25 2011
(PARI) a(n)=lcm(vector(n, k, 2*k-1)) \\ Charles R Greathouse IV, Nov 20 2012
(Python) # generates initial segment of sequence
from math import gcd
from itertools import accumulate
def lcm(a, b): return a * b // gcd(a, b)
def aupton(nn): return list(accumulate((2*i+1 for i in range(nn)), lcm))
print(aupton(23)) # Michael S. Branicky, Mar 28 2022

Crossrefs

Cf. A007509, A025550, A075135. The numerators are in A074599.

Cf. A003418 (LCM of {1..n}).

Cf. A005408, A350670.

Sequence in context: A293996 A229726 A145624 * A352395 A350670 A220747

Adjacent sequences: A025544 A025545 A025546 * A025548 A025549 A025550

Keyword

easy,nice,nonn

Author

Clark Kimberling

Status

approved