A217858 Odd part of lcm(1,2,3,...,n).

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

Offset: 1

Author

Joerg Arndt, Oct 13 2012

Keywords

• nonn

Examples

			a(8) is the least common multiple of {1,3,5,7}.
		

Crossrefs

Cf. A003418, A025547, A128501, A216917.

Programs

Maple

A217858 := n -> ilcm(op(select(j->j mod 2 = 1, [$1..n]))):
seq(A217858(i), i = 1..33); # Peter Luschny, Oct 15 2012

Mathematica

a[n_] := LCM @@ Select[Range[n], OddQ]; Array[a, 33] (* Jean-François Alcover, Jun 27 2019 *)

PARI

A003418(n) = lcm(vector(n,k, k));
A000265(n) = n/2^valuation(n,2);
a(n) = A000265( A003418(n) );

Sage

def A217858(n): return lcm([j for j in (1..n) if is_odd(j)])
[A217858(n) for n in (1..33)]  # Peter Luschny, Oct 15 2012

Formula

a(n) = A000265( A003418(n) ).

a(n) = lcm_{1 <= k <= n, k odd}. - Peter Luschny, Oct 15 2012

a(n) = A025547(floor((n+1)/2)). - Georg Fischer, Nov 29 2022