A230313 Numbers n such that A031971(47058*n) <> n (mod 47058*n).

1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73

Offset: 1

Author

José María Grau Ribas, Nov 16 2013

Keywords

• nonn

Comments

The asymptotic density lies in the interval [0.919943, 0.943954].

Complement of A229312.

The numbers in A230311 are the values of k such that the set {n : A031971(k*n)== n (mod k*n)} is nonempty.

Links

• Jose María Grau, A. M. Oller-Marcen, and J. Sondow, On the congruence 1^n + 2^n +... + n^n = d (mod n), where d divides n

Crossrefs

Cf. A031971, A230311.

Cf. A231562 (numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n)).

Cf. A229312 (numbers n such that A031971(47058*n) == n (mod 47058*n)).

Cf. A229300 (numbers n such that A031971(1806*n)== n (mod n*1806)).

Cf. A229301 (numbers n such that A031971(42*n) == n (mod 42*n)).

Cf. A229302 (numbers n such that A031971(6*n) == n (mod 6*n)).

Cf. A229303 (numbers n such that A031971(2*n) == n (mod 2*n)).

Cf. A229313 (numbers n such that A031971(47058*n) <> n (mod 47058*n)).

Cf. A229304 (numbers n such that A031971(1806*n) <> n (mod n*1806)).

Cf. A229305 (numbers n such that A031971(42*n) <> n (mod 42*n)).

Cf. A229306 (numbers n such that A031971(6*n) <> n (mod 6*n)).

Cf. A229307 (numbers n such that A031971(2*n) <> n (mod 2*n)).

Cf. A229308 (primitive numbers in A229304).

Cf. A229309 (primitive numbers in A229305).

Cf. A229310 (primitive numbers in A229306).

Cf. A229311 (primitive numbers in A229307).

Programs

Mathematica

fa = FactorInteger; Car[k_, n_] := Mod[n - Sum[If[IntegerQ[k/(fa[n][[i,
   1]] - 1)], n/fa[n][[i, 1]], 0], {i, 1, Length[fa[n]]}], n]; supercar[k_, n_] := If[k == 1 || Mod[k, 2] == 0 || Mod[n, 4] > 0, Car[k,n], Mod[Car[k, n] - n/2, n]]; Select[Range[1000], !supercar[47058*#, 47058*#] == # &]