A056839 Squarefree part of lcm(1,...,n).

1, 1, 2, 6, 3, 15, 15, 105, 210, 70, 70, 770, 770, 10010, 10010, 10010, 5005, 85085, 85085, 1616615, 1616615, 1616615, 1616615, 37182145, 37182145, 7436429, 7436429, 22309287, 22309287, 646969323, 646969323, 20056049013, 40112098026, 40112098026, 40112098026

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Formula

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

Example

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.

Maple

b:= proc(n) b(n):= `if`(n=0, 1, ilcm(b(n-1), n)) end:
a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(b(n))[2]):
seq(a(n), n=0..40);  # Alois P. Heinz, Apr 01 2016

Mathematica

{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 *)

Prog

(PARI) a(n) = core(lcm(vector(n, k, k))); \\ Michel Marcus, Oct 27 2017

Crossrefs

Cf. A007913, A003418, A000196.

Sequence in context: A368823 A372000 A121566 * A302033 A337643 A071301

Adjacent sequences: A056836 A056837 A056838 * A056840 A056841 A056842

Keyword

nonn

Author

Labos Elemer, Aug 29 2000

Extensions

a(0)=1 inserted by Alois P. Heinz, Apr 01 2016

Edited by Jon E. Schoenfield, Jul 09 2018

Status

approved