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A061006
a(n) = (n-1)! mod n.
11
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
OFFSET
1,3
COMMENTS
It appears that a(n) = (n!*h(n)) mod n, where h(n) = Sum_{k = 1..n} 1/k. - Gary Detlefs, Sep 04 2010
Indeed: It is easy to show n!*h(n) - (n-1)! = n*(n-1)!*h(n-1). Since (n-1)!*h(n-1) is integral, n!*h(n) == (n-1)! mod n. - Franz Vrabec, Apr 08 2017
LINKS
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.
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: A127786 A030207 A366561 * A080736 A326127 A276151
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Apr 12 2001
STATUS
approved