login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209389 Product of positive odd integers smaller than n and relatively prime to n, taken Modd n. A209388(n) (Modd n). 1
0, 1, 1, 3, 3, 5, 1, 7, 1, 9, 1, 1, 5, 13, 11, 15, 13, 17, 1, 1, 13, 21, 1, 1, 7, 25, 1, 1, 17, 1, 1, 31, 23, 33, 29, 1, 31, 37, 25, 1, 9, 1, 1, 1, 19, 45, 1, 1, 1, 49, 35, 1, 23, 53, 21, 1, 37, 57, 1, 1, 11, 61, 55, 63, 1, 1, 1, 1, 47, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For Modd n (not to be confused with mod n) see a comment on A203571.

See A209388 for the number of elements of the reduced residue class Modd n, called delta(n).

a(prime(n)) = (prime(n)-2)!! Modd prime(n) = 1 if n=1 or (prime(n)-1)/2 is odd, and = r(prime(n)) if (prime(n)-1)/2 is even. Here r(prime(n)) is the smallest positive nontrivial solution of x^2==1 (Modd prime(n)), which exists only for primes of the form 4*k+1 given in A002144. For r(prime(n)) see A206549. This is the analog of Wilson's theorem for Modd prime(n).

For (prime(n)-2)!! see A207332. [Wolfdieter Lang, Mar 28 2012]

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(n) = A209388(n) (Modd n), n>=1.

EXAMPLE

a(1) = 1 (Modd 1) = -1 (mod 1) = 0, because floor(1/1)=1 is odd. a(4)= 1*3 (Modd 4) = 3, a(15) = 1*7*11*13 (Modd 15) = 1001 (Modd 15) = 1001 (mod 15) because floor(1001/15) = 66 is even, hence a(15) = 11.

CROSSREFS

Cf. A209388, A160377 (mod n analog).

Sequence in context: A079887 A131843 A205550 * A337544 A105104 A229087

Adjacent sequences:  A209386 A209387 A209388 * A209390 A209391 A209392

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Mar 10 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)