

A209388


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


2



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


LINKS

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


FORMULA

a(n) = product(2*k+1, k from {0,1,...,floor((n2)/2)} and gcd(2*k+1,n) =1). a(1):=1 (empty product).
a(n) = product(k, k from {1,...,n1} and gcd(k,2*n) = 1). a(1):=1 (empty product).


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 *)


CROSSREFS

Cf. A001783 (mod n analog), A207332, A209339.
Sequence in context: A069834 A064038 A051684 * A195583 A139431 A144423
Adjacent sequences: A209385 A209386 A209387 * A209389 A209390 A209391


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Mar 10 2012


STATUS

approved



