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

1,3

Links

Table of n, a(n) for n=1..33.

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A003418, A025547, A128501, A216917.

Sequence in context: A362531 A129356 A290344 * A185275 A055634 A133221

Adjacent sequences: A217855 A217856 A217857 * A217859 A217860 A217861

Keyword

nonn

Author

Joerg Arndt, Oct 13 2012

Status

approved