A209389 Product of positive odd integers smaller than n and relatively prime to n, taken Modd n. A209388(n) (Modd n).

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

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