A239062 -id:A239062 - cp's OEIS frontend

A239061 Number of integers x, 1 <= x <= n, such that x^x == 1 (mod n).

1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 5, 2, 4, 1, 4, 1, 4, 1, 3, 3, 2, 1, 2, 3, 2, 2, 4, 1, 3, 1, 5, 1, 6, 1, 3, 2, 4, 1, 5, 1, 6, 3, 5, 1, 2, 1, 4, 1, 6, 2, 3, 1, 5, 2, 3, 3, 3, 1, 5, 3, 3, 1, 9, 2, 5, 1, 5, 2, 4, 1, 5, 3, 5, 3, 10, 1, 5, 1, 2, 1, 3, 1, 10, 3

Offset: 1

José María Grau Ribas, Mar 09 2014

nonn

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A239062, A239063 (indices of 1's).

gg1[n_] := Sum[If[PowerMod[x, x, n] == Mod[1, n], 1, 0], {x, n}];Array[gg1,200]

A338445 Numbers m with integer solution to x^x == (x+1)^(x+1) (mod m) with 1<=x

Original entry on oeis.org

3, 11, 13, 19, 23, 29, 31, 43, 49, 53, 57, 59, 61, 67, 71, 73, 77, 79, 83, 85, 89, 91, 93, 97, 101, 103, 109, 113, 127, 129, 131, 133, 141, 143, 147, 149, 151, 157, 161, 163, 167, 169, 173, 177, 179, 183, 187, 197, 199, 201, 203, 205, 211, 217, 229, 235, 237, 239

Offset: 1

Owen C. Keith, Oct 28 2020

nonn

Some values of m have multiple solutions.
For example, for m = 49, 25^25 == 26^26 (mod 49) and 37^37 == 38^38 (mod 49).
All terms are odd. - Robert Israel, Nov 25 2020

			3 is a term because 1^1 == 2^2 (mod 3).
11 is a term because 8^8 == 9^9 (mod 11).
13 is a term because 8^8 == 9^9 (mod 13).

Robert Israel, Table of n, a(n) for n = 1..10000

Similar sequences: A174824, A239061, A239062, A239063.

filter:= proc(n) local x,y,z;
  y:= 1;
  for x from 2 to n-1 do
    z:= x &^ x mod n;
    if z = y then return true fi;
    y:= z
  od;
  false
end proc:
select(filter, [$2..1000]); # Robert Israel, Nov 25 2020

seqQ[n_] := AnyTrue[Range[n - 1], PowerMod[#, #, n] == PowerMod[# + 1, # + 1, n] &]; Select[Range[240], seqQ] (* Amiram Eldar, Oct 28 2020 *)

isok(m)=sum(i=1, m-1, Mod(i,m)^i == Mod((i+1),m)^(i+1)) \\ Andrew Howroyd, Oct 28 2020

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A239061 Number of integers x, 1 <= x <= n, such that x^x == 1 (mod n).

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A338445 Numbers m with integer solution to x^x == (x+1)^(x+1) (mod m) with 1<=x

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