A209388 Product of positive odd integers smaller than n and relatively prime to n.

1, 1, 1, 3, 3, 5, 15, 105, 35, 189, 945, 385, 10395, 19305, 1001, 2027025, 2027025, 85085, 34459425, 8729721, 230945, 1249937325, 13749310575, 37182145, 4216455243, 608142583125, 929553625, 1452095555625, 213458046676875, 215656441, 6190283353629375

Offset: 1

Author

Wolfdieter Lang, Mar 10 2012

Keywords

• nonn
• easy

Comments

This is the product over the smallest positive representatives of the odd reduced residue class Modd n. For Modd n (not to be confused with mod n) see a comment on A203571. This reduced residue class has delta(n)=A055034(n) members.

The Moddn values of this sequence are given in A209339.

Examples

			a(4) = 1*3 = 3.
a(5) = 1*3 = 3.
a(15) = 1*7*11*13 = 1001.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A001783 (mod n analog), A207332, A209339.

Programs

Mathematica

Table[Times @@ Select[Range[1, n, 2], GCD[n, #] == 1 &], {n, 40}] (* T. D. Noe, Mar 12 2012 *)

PARI

a(n) = prod(k=1, n, if (k % 2, k, 1)); \\ Michel Marcus, Mar 12 2022

Formula

a(n) = product(2*k+1, k from {0,1,...,floor((n-2)/2)} and gcd(2*k+1,n) =1). a(1):=1 (empty product).

a(n) = product(k, k from {1,...,n-1} and gcd(k,2*n) = 1). a(1):=1 (empty product).

a(prime(n)) = (prime(n)-2)!! = A207332(n), for primes prime(n)=A000040(n).