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

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 53, 54, 56, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 81

Offset

1,2

Comments

Complement of A229304.

The asymptotic density is in [0.7747,0.812570].

The numbers k = 1, 2, 6, 42, 1806, 47058, 2214502422, 8490421583559688410706771261086 = A230311 are the only values of k such that the set {n: A031971(k*n) == n (mod k*n)} is nonempty. Its smallest element is n = 1, 1, 1, 1, 1, 5, 5, 39607528021345872635 = A231409. (Comment corrected and expanded by Jonathan Sondow, Dec 10 2013.)

Links

Table of n, a(n) for n=1..67.

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

Mathematica

g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[100], g[1806*#] == # &]

Crossrefs

Cf. A031971, A231409.

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).

Cf. A054377 (primary pseudoperfect numbers).

Sequence in context: A069570 A279367 A020731 * A229301 A277061 A361978

Adjacent sequences: A229297 A229298 A229299 * A229301 A229302 A229303

Keyword

nonn

Author

José María Grau Ribas, Sep 19 2013

Status

approved