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

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, 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, 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

Offset: 1

Author

José María Grau Ribas, Mar 09 2014

Keywords

• nonn

Examples

			From _Michael De Vlieger_, Sep 23 2017: (Start)
Table of records a(n) and first positions n:
   i       n    a(n)
-------------------
   1       1      1
   2       4      2
   3       8      3
   4      16      7
   5      27      9
   6      32     15
   7      64     31
   8     128     62
   9     243     80
  10     256    126
  11     512    253
  12    1024    509
  13    2048   1020
  14    4096   2044
  15    6561   2185
  16    8192   4092
  17   16384   8188
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A239061, A239063, A005117 (indices of 1's).

Programs

Mathematica

gg0[n_] := Sum[If[Mod[x^x , n] == 0, 1, 0], {x, n}];Array[gg0,200]
(* or *)
Array[Sum[Boole[PowerMod[x, x, #] == 0], {x, #}] &, 10^4] (* or *)
Table[Count[Range@ n, k_ /; PowerMod[k, k, n] == 0], {n, 200}] (* Michael De Vlieger, Sep 23 2017 *)

PARI

A239062(n) = sum(x=1,n, if(0 == Mod(x^x, n), 1, 0)); \\ Antti Karttunen, Sep 23 2017, after the Mathematica-program.

Extensions

More terms from Antti Karttunen, Sep 23 2017