cp's OEIS Frontend

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

%I A217858 #23 Nov 29 2022 08:35:59
%S A217858 1,1,3,3,15,15,105,105,315,315,3465,3465,45045,45045,45045,45045,
%T A217858 765765,765765,14549535,14549535,14549535,14549535,334639305,
%U A217858 334639305,1673196525,1673196525,5019589575,5019589575,145568097675,145568097675,4512611027925,4512611027925,4512611027925
%N A217858 Odd part of lcm(1,2,3,...,n).
%F A217858 a(n) = A000265( A003418(n) ).
%F A217858 a(n) = lcm_{1 <= k <= n, k odd}. - _Peter Luschny_, Oct 15 2012
%F A217858 a(n) = A025547(floor((n+1)/2)). - _Georg Fischer_, Nov 29 2022
%e A217858 a(8) is the least common multiple of {1,3,5,7}.
%p A217858 A217858 := n -> ilcm(op(select(j->j mod 2 = 1, [$1..n]))):
%p A217858 seq(A217858(i), i = 1..33); # _Peter Luschny_, Oct 15 2012
%t A217858 a[n_] := LCM @@ Select[Range[n], OddQ]; Array[a, 33] (* _Jean-François Alcover_, Jun 27 2019 *)
%o A217858 (PARI)
%o A217858 A003418(n) = lcm(vector(n,k, k));
%o A217858 A000265(n) = n/2^valuation(n,2);
%o A217858 a(n) = A000265( A003418(n) );
%o A217858 (Sage)
%o A217858 def A217858(n): return lcm([j for j in (1..n) if is_odd(j)])
%o A217858 [A217858(n) for n in (1..33)]  # _Peter Luschny_, Oct 15 2012
%Y A217858 Cf. A003418, A025547, A128501, A216917.
%K A217858 nonn
%O A217858 1,3
%A A217858 _Joerg Arndt_, Oct 13 2012