A056839 - OEIS

%I #19 Jul 09 2018 01:42:09

%S 1,1,2,6,3,15,15,105,210,70,70,770,770,10010,10010,10010,5005,85085,

%T 85085,1616615,1616615,1616615,1616615,37182145,37182145,7436429,

%U 7436429,22309287,22309287,646969323,646969323,20056049013,40112098026,40112098026,40112098026

%N Squarefree part of lcm(1,...,n).

%H Alois P. Heinz, <a href="/A056839/b056839.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) = A007913(A003418(n)) = lcm(1..n)/lcm(1..q)^2, where q = floor(sqrt(n)) = A000196(n).

%e n=65: lcm(1..65) = 1182266884102822267511361600, floor(sqrt(65))=8, lcm(1..8) = 8*3*5*7 = 840; a(65) = lcm(1..65)/lcm(1..8)^2 = 1675548305134385299761 is squarefree.

%p b:= proc(n) b(n):= `if`(n=0, 1, ilcm(b(n-1), n)) end:

%p a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(b(n))[2]):

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Apr 01 2016

%t {1}~Join~Array[Sqrt[#] /. (c_: 1) a_^(b_: 0) :> (c a^b)^2 &[LCM @@ Range@ #] &, 34] (* _Michael De Vlieger_, Oct 26 2017, after _Bill Gosper_ at A007913 *)

%o (PARI) a(n) = core(lcm(vector(n, k, k))); \\ _Michel Marcus_, Oct 27 2017

%Y Cf. A007913, A003418, A000196.

%K nonn

%O 0,3

%A _Labos Elemer_, Aug 29 2000

%E a(0)=1 inserted by _Alois P. Heinz_, Apr 01 2016

%E Edited by _Jon E. Schoenfield_, Jul 09 2018