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

1,4

Links

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

Example

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A152798 A079115 A072906 * A341052 A201160 A302538

Adjacent sequences: A239059 A239060 A239061 * A239063 A239064 A239065

Keyword

nonn

Author

José María Grau Ribas, Mar 09 2014

Extensions

More terms from Antti Karttunen, Sep 23 2017

Status

approved