A229300 - OEIS

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

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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)).