A119619 a(n) = Product_{i=1..n} i / gcd(i,n).

1, 1, 2, 3, 24, 10, 720, 315, 4480, 4536, 3628800, 11550, 479001600, 13899600, 43051008, 638512875, 20922789888000, 1905904000, 6402373705728000, 118794043368, 68108451840000, 4535772564960000, 1124000727777607680000

Offset: 1

Author

Martin Fuller, Jun 06 2006

Keywords

• nonn

Comments

If p is prime, then a(p) = (p-1)!. - Stefan Steinerberger, Jun 08 2006

Crossrefs

Cf. A067911.

Cf. A000142, A067911.

Programs

Magma

[&*[&*[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(n)]: n in [1..100]]; // Jaroslav Krizek, Dec 28 2016

Maple

a:=n->mul(numer (k/n), k=1..n): seq(a(n), n=1..23); # Zerinvary Lajos, Apr 26 2008

Mathematica

a[n_] := Product[i/GCD[i, n], {i, 1, n}]; Table[a[n], {n, 1, 30}] (* Stefan Steinerberger, Jun 08 2006 *)
Table[Product[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 23}] (* Michael De Vlieger, Dec 28 2016 *)

PARI

a(n) = prod(i=1,n,i/gcd(i,n))

Formula

a(n) = Product_{d|n} pxi(d), where pxi(m) = is the product of totatives of m (A001783). - Jaroslav Krizek, Dec 28 2016

a(n) = A000142(n)/A067911(n). - Ridouane Oudra, Nov 20 2021

Extensions

More terms from Stefan Steinerberger, Jun 08 2006