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

1,4

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.

Links

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

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).

Example

a(4)= 1*3 = 3, a(5) = 1*3 =3, a(15) = 1*7*11*13 = 1001, delta(15)=phi(2*15)/2) = 1*2*4/2 = 4 = A055034(15).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A069834 A064038 A051684 * A195583 A370973 A139431

Adjacent sequences: A209385 A209386 A209387 * A209389 A209390 A209391

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 10 2012

Status

approved