A066570 Product of numbers <= n that have a prime factor in common with n.

1, 2, 3, 8, 5, 144, 7, 384, 162, 19200, 11, 1244160, 13, 4515840, 1458000, 10321920, 17, 75246796800, 19, 278691840000, 1080203040, 899245670400, 23, 16686729658368000, 375000, 663152807116800, 7142567040, 209964381084057600, 29, 1229978843118305280000000

Offset

1,2

Comments

Empty product, 1, for n = 1.

a(p) = p if p is a prime.

Links

T. D. Noe, Table of n, a(n) for n = 1..200

Formula

a(n) = n!/A001783(n).

a(n) = Gauss_factorial(n, 1)/Gauss_factorial(n, n) (see A216919). - Peter Luschny, Oct 02 2012

Example

a(7) = 7, a(9) = 3*6*9 = 162.

Maple

A066570 := proc(n) local i; mul(i, i=remove(k->igcd(n, k)=1, [$1..n])) end: # Peter Luschny, Oct 11 2011

Mathematica

Table[Times @@ Select[Range[2, n], GCD[#, n] > 1 &], {n, 30}] (* T. D. Noe, Oct 04 2012 *)

Prog

(Sage)
def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)
def A066570(n): return Gauss_factorial(n, 1)/Gauss_factorial(n, n)
[A066570(n) for n in (1..30)] # Peter Luschny, Oct 02 2012
(PARI) a(n) = prod(k=1, n, if (gcd(k, n) != 1, k, 1)); \\ Michel Marcus, Nov 02 2017

Crossrefs

Cf. A001783, A216919.

Sequence in context: A067911 A243103 A051696 * A073656 A047930 A349100

Adjacent sequences: A066567 A066568 A066569 * A066571 A066572 A066573

Keyword

nonn,easy

Author

Amarnath Murthy, Dec 19 2001

Status

approved