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A066570 Product of numbers <= n that have a prime factor in common with n. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A073875

Adjacent sequences:  A066567 A066568 A066569 * A066571 A066572 A066573

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Dec 19 2001

STATUS

approved

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Last modified December 11 19:09 EST 2017. Contains 295919 sequences.