cp's OEIS Frontend

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

%I A209388 #26 Oct 26 2024 04:07:50
%S A209388 1,1,1,3,3,5,15,105,35,189,945,385,10395,19305,1001,2027025,2027025,
%T A209388 85085,34459425,8729721,230945,1249937325,13749310575,37182145,
%U A209388 4216455243,608142583125,929553625,1452095555625,213458046676875,215656441,6190283353629375
%N A209388 Product of positive odd integers smaller than n and relatively prime to n.
%C A209388 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.
%C A209388 The Moddn values of this sequence are given in A209339.
%H A209388 Vincenzo Librandi, <a href="/A209388/b209388.txt">Table of n, a(n) for n = 1..200</a>
%F A209388 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).
%F A209388 a(n) = product(k, k from {1,...,n-1} and gcd(k,2*n) = 1). a(1):=1 (empty product).
%F A209388 a(prime(n)) = (prime(n)-2)!! = A207332(n), for primes prime(n)=A000040(n).
%e A209388 a(4) = 1*3 = 3.
%e A209388 a(5) = 1*3 = 3.
%e A209388 a(15) = 1*7*11*13 = 1001.
%t A209388 Table[Times @@ Select[Range[1, n, 2], GCD[n, #] == 1 &], {n, 40}] (* _T. D. Noe_, Mar 12 2012 *)
%o A209388 (PARI) a(n) = prod(k=1, n, if (k % 2, k, 1)); \\ _Michel Marcus_, Mar 12 2022
%Y A209388 Cf. A001783 (mod n analog), A207332, A209339.
%K A209388 nonn,easy
%O A209388 1,4
%A A209388 _Wolfdieter Lang_, Mar 10 2012