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

5, 15, 25, 45, 55, 65, 75, 85, 95, 115, 125, 135, 145, 155, 165, 185, 195, 205, 215, 225, 255, 265, 275, 295, 305, 325, 345, 355, 365, 375, 395, 405, 415, 425, 435, 445, 465, 475, 485, 495, 505, 515, 535, 545, 555, 565, 575, 585, 605, 615, 625, 635, 645, 655

Offset: 1

Author

José María Grau Ribas, Oct 20 2013

Keywords

• nonn

Comments

The number 47058 occurring in the name is the sixth term of A230311.

The asymptotic density lies in the interval [0.0560465, 0.0800567].

Complement of A230313 .

For n<235295, A031971(47058*n) == n (mod 47058*n) if and only if A031971(2214502422*n) <> n (mod 2214502422*n).

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*#] == # &]