A217858 - OEIS

%I #23 Nov 29 2022 08:35:59

%S 1,1,3,3,15,15,105,105,315,315,3465,3465,45045,45045,45045,45045,

%T 765765,765765,14549535,14549535,14549535,14549535,334639305,

%U 334639305,1673196525,1673196525,5019589575,5019589575,145568097675,145568097675,4512611027925,4512611027925,4512611027925

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

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

%F a(n) = lcm_{1 <= k <= n, k odd}. - _Peter Luschny_, Oct 15 2012

%F a(n) = A025547(floor((n+1)/2)). - _Georg Fischer_, Nov 29 2022

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

%p A217858 := n -> ilcm(op(select(j->j mod 2 = 1, [$1..n]))):

%p seq(A217858(i), i = 1..33); # _Peter Luschny_, Oct 15 2012

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

%o (PARI)

%o A003418(n) = lcm(vector(n,k, k));

%o A000265(n) = n/2^valuation(n,2);

%o a(n) = A000265( A003418(n) );

%o (Sage)

%o def A217858(n): return lcm([j for j in (1..n) if is_odd(j)])

%o [A217858(n) for n in (1..33)]  # _Peter Luschny_, Oct 15 2012

%Y Cf. A003418, A025547, A128501, A216917.

%K nonn

%O 1,3

%A _Joerg Arndt_, Oct 13 2012