

A061006


a(n) = (n1)! 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
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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)  (n1)! = n*(n1)!*h(n1). Since (n1)!*h(n1) is integral, n!*h(n) == (n1)! mod n.  Franz Vrabec, Apr 08 2017


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) = (n1)*A061007(n) = (n1)*A010051(n).


EXAMPLE

a(4) = 2 since (41)! = 6 = 2 mod 4.
a(5) = 4 since (51)! = 24 = 4 mod 5.
a(6) = 0 since (61)! = 120 = 0 mod 6.


MAPLE

P:=proc(n) local a, i, k, w; for i from 1 by 1 to n do w:=((i1)! 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), n1, 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



