

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
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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



