login
Product of numbers < n which do not divide n (or 1 if no such numbers exist).
7

%I #31 Jun 26 2022 02:19:02

%S 1,1,2,3,24,20,720,630,13440,36288,3628800,277200,479001600,444787200,

%T 5811886080,20432412000,20922789888000,1097800704000,6402373705728000,

%U 304112751022080,115852476579840000,2322315553259520000

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

%H Reinhard Zumkeller, <a href="/A055067/b055067.txt">Table of n, a(n) for n = 1..250</a>

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

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

%t Table[Apply[Times, Complement[Range[n], Divisors[n]]], {n, 1, 20}] (* _Geoffrey Critzer_, Dec 13 2014 *)

%t a[n_] := n!/n^(DivisorSigma[0, n]/2); Array[a, 25] (* _Amiram Eldar_, Jun 26 2022 *)

%o (Haskell)

%o a055067 n = product [k | k <- [1..n], mod n k /= 0]

%o -- _Reinhard Zumkeller_, Feb 06 2012

%o (PARI) a(n) = n!/vecprod(divisors(n)); \\ _Michel Marcus_, Dec 26 2021

%o (Python)

%o from math import factorial, isqrt

%o from sympy import divisor_count

%o 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

%Y Cf. A024816.

%Y Cf. A173540, A072046.

%Y Cf. A000142, A007955.

%K easy,nonn

%O 1,3

%A _Henry Bottomley_, Jun 12 2000

%E More terms from _David Wasserman_, Mar 15 2002