A055067 Product of numbers < n which do not divide n (or 1 if no such numbers exist).

1, 1, 2, 3, 24, 20, 720, 630, 13440, 36288, 3628800, 277200, 479001600, 444787200, 5811886080, 20432412000, 20922789888000, 1097800704000, 6402373705728000, 304112751022080, 115852476579840000, 2322315553259520000

Offset: 1

Author

Henry Bottomley, Jun 12 2000

Keywords

• easy
• nonn

Examples

			a(5)=2*3*4=24, a(6)=4*5=20.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A024816.

Cf. A173540, A072046.

Cf. A000142, A007955.

Programs

Haskell

a055067 n = product [k | k <- [1..n], mod n k /= 0]
-- Reinhard Zumkeller, Feb 06 2012

Mathematica

Table[Apply[Times, Complement[Range[n], Divisors[n]]], {n, 1, 20}] (* Geoffrey Critzer, Dec 13 2014 *)
a[n_] := n!/n^(DivisorSigma[0, n]/2); Array[a, 25] (* Amiram Eldar, Jun 26 2022 *)

PARI

a(n) = n!/vecprod(divisors(n)); \\ Michel Marcus, Dec 26 2021

Python

from math import factorial, isqrt
from sympy import divisor_count
def A055067(n): return factorial(n)//(isqrt(n)**c if (c:=divisor_count(n)) & 1 else n**(c//2)) # Chai Wah Wu, Jun 25 2022

Formula

a(n) = A000142(n)/A007955(n).

Extensions

More terms from David Wasserman, Mar 15 2002