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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A024816.

Cf. A173540, A072046.

Cf. A000142, A007955.

Sequence in context: A099617 A092043 A343206 * A037319 A032811 A092049

Adjacent sequences: A055064 A055065 A055066 * A055068 A055069 A055070

Keyword

easy,nonn

Author

Henry Bottomley, Jun 12 2000

Extensions

More terms from David Wasserman, Mar 15 2002

Status

approved