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A209388 Product of positive odd integers smaller than n and relatively 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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 10 2012
STATUS
approved

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Last modified June 21 06:22 EDT 2024. Contains 373540 sequences. (Running on oeis4.)