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A061006 a(n) = (n-1)! mod n. 9
0, 1, 2, 2, 4, 0, 6, 0, 0, 0, 10, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 22, 0, 0, 0, 0, 0, 28, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 40, 0, 42, 0, 0, 0, 46, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 58, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 70, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 82, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It appears that a(n) = (n!*h(n)) mod n, where h(n) = sum(1/k, k = 1..n). - Gary Detlefs, Sep 04 2010

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Wikipedia, Wilson's theorem

FORMULA

a(4) = 2, a(p) = p - 1 for p prime (Wilson's_theorem), a(n) = 0 otherwise. Apart from n = 4, a(n) = (n-1)*A061007(n) = (n-1)*A010051(n).

EXAMPLE

a(4) = 2 since (4-1)! = 6 = 2 mod 4.

a(5) = 4 since (5-1)! = 24 = 4 mod 5.

a(6) = 0 since (6-1)! = 120 = 0 mod 6.

MAPLE

P:=proc(n) local a, i, k, w; for i from 1 by 1 to n do w:=((i-1)! mod i); print(w); od; end: P(1000); # Paolo P. Lava, Apr 23 2007

MATHEMATICA

Table[Mod[(n - 1)!, n], {n, 100}] (* Alonso del Arte, Feb 16 2014 *)

PROG

(PARI) a(n)=if(isprime(n), n-1, if(n==4, 2, 0)) \\ Charles R Greathouse IV, Mar 31 2014

CROSSREFS

Positive for all but the first term of A046022. Cf. A000040, A000142, A061007, A061008, A061009.

Sequence in context: A246816 A127786 A030207 * A080736 A276151 A144412

Adjacent sequences:  A061003 A061004 A061005 * A061007 A061008 A061009

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Apr 12 2001

STATUS

approved

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Last modified March 29 03:29 EDT 2017. Contains 284250 sequences.