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A239062 Number of integers x, 1 <= x <= n, such that x^x == 0 (mod n).

%I A239062 #23 Apr 05 2021 03:54:47
%S A239062 1,1,1,2,1,1,1,3,3,1,1,2,1,1,1,7,1,3,1,2,1,1,1,4,5,1,9,2,1,1,1,15,1,1,
%T A239062 1,6,1,1,1,4,1,1,1,2,3,1,1,8,7,5,1,2,1,9,1,4,1,1,1,2,1,1,3,31,1,1,1,2,
%U A239062 1,1,1,12,1,1,5,2,1,1,1,8,26,1,1,2,1,1,1,4,1,3,1,2,1,1,1,16,1,7,3,10,1,1,1,4,1
%N A239062 Number of integers x, 1 <= x <= n, such that x^x == 0 (mod n).
%H A239062 Antti Karttunen, <a href="/A239062/b239062.txt">Table of n, a(n) for n = 1..10000</a>
%e A239062 From _Michael De Vlieger_, Sep 23 2017: (Start)
%e A239062 Table of records a(n) and first positions n:
%e A239062    i       n    a(n)
%e A239062 -------------------
%e A239062    1       1      1
%e A239062    2       4      2
%e A239062    3       8      3
%e A239062    4      16      7
%e A239062    5      27      9
%e A239062    6      32     15
%e A239062    7      64     31
%e A239062    8     128     62
%e A239062    9     243     80
%e A239062   10     256    126
%e A239062   11     512    253
%e A239062   12    1024    509
%e A239062   13    2048   1020
%e A239062   14    4096   2044
%e A239062   15    6561   2185
%e A239062   16    8192   4092
%e A239062   17   16384   8188
%e A239062 (End)
%t A239062 gg0[n_] := Sum[If[Mod[x^x , n] == 0, 1, 0], {x, n}];Array[gg0,200]
%t A239062 (* or *)
%t A239062 Array[Sum[Boole[PowerMod[x, x, #] == 0], {x, #}] &, 10^4] (* or *)
%t A239062 Table[Count[Range@ n, k_ /; PowerMod[k, k, n] == 0], {n, 200}] (* _Michael De Vlieger_, Sep 23 2017 *)
%o A239062 (PARI) A239062(n) = sum(x=1,n, if(0 == Mod(x^x, n), 1, 0)); \\ _Antti Karttunen_, Sep 23 2017, after the Mathematica-program.
%Y A239062 Cf. A239061, A239063, A005117 (indices of 1's).
%K A239062 nonn
%O A239062 1,4
%A A239062 _José María Grau Ribas_, Mar 09 2014
%E A239062 More terms from _Antti Karttunen_, Sep 23 2017