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%I #14 Feb 19 2014 13:47:05
%S 0,1,1,2,1,4,2,4,3,4,1,7,2,5,7,6,3,8,2,9,7,5,2,13,5,8,3,11,2,14,3,6,8,
%T 8,9,13,2,7,9,17,5,18,3,11,13,5,2,19,9,12,11,13,1,8,11,18,9,7,1,27,4,
%U 7,20,10,16,18,3,13,8,21,2,23,5,6,16,14,13,23,4,27,9,11,1,31,13,10,12,20
%N Number of values of s, 0 < s <= n-1, such that s^s == s (mod n).
%C Note that a(1) = 0 by definition. - _Harry J. Smith_, Oct 15 2009
%H Harry J. Smith and T. D. Noe, <a href="/A065295/b065295.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%e For n=5 we have (1^1) mod 5 = 1, (2^2) mod 5 = 4, (3^3) mod 5 = 2, (4^4) mod 5 = 1. Only for s=1 does (s^s) mod 5=s, so a(5)=1
%t f[p_] := Module[{x = Range[p-1]}, Count[PowerMod[x, x, p] - x, 0]]; Table[f[n], {n, 100}] (* _T. D. Noe_, Feb 19 2014 *)
%o (PARI) { for (n=1, 1000, a=0; for (s=1, n - 1, if (s^s % n == s, a++)); if (n==1, a=0); write("b065295.txt", n, " ", a) ) } [_Harry J. Smith_, Oct 15 2009]
%Y Cf. A065296.
%K nonn
%O 1,4
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 28 2001
%E Definition revised by _N. J. A. Sloane_, Oct 15 2009.
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