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A067462 a(n) = (1! + 2! + ... + (n-1)!) mod n.

%I A067462 #22 Jan 23 2023 15:04:16
%S A067462 0,1,0,1,3,3,5,1,0,3,0,9,9,5,3,9,12,9,8,13,12,11,20,9,13,9,9,5,16,3,1,
%T A067462 25,0,29,33,9,4,27,9,33,3,33,15,33,18,43,17,9,47,13,12,9,12,9,33,33,
%U A067462 27,45,27,33,21,1,54,25,48,33,64,29,66,33,67,9,54,41,63,65,33,9,19,73,63
%N A067462 a(n) = (1! + 2! + ... + (n-1)!) mod n.
%H A067462 A.H.M. Smeets, <a href="/A067462/b067462.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from T. D. Noe)
%t A067462 Mod[ #[[1]], #[[2]]]&/@Transpose[{Rest[FoldList[Plus, 0, Factorial[Range[90]]]], Range[90]}]
%t A067462 Table[Mod[Total[Range[n-1]!],n],{n,90}] (* _Harvey P. Dale_, Jan 23 2023 *)
%o A067462 (PARI) a(n) = my(s=0, p=1); for (i=1, n-1, f = Mod(i, n); p*=f; s += p); lift(s); \\ _Michel Marcus_, Aug 19 2019
%o A067462 (Python)
%o A067462 n = 0
%o A067462 while n < 200:
%o A067462     n,f,fs,i = n+1,1,0,1
%o A067462     while i < n:
%o A067462         f,i = (f*i)%n,i+1
%o A067462         fs = (fs+f)%n
%o A067462     print(n,fs) # _A.H.M. Smeets_, Aug 19 2019
%Y A067462 Cf. A049782.
%K A067462 easy,nonn
%O A067462 1,5
%A A067462 _Alex Fink_, Feb 24 2002