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 A061006 a(n) = (n-1)! mod n. 10
 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_{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 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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