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%I A229302 #20 Dec 11 2015 22:06:40
%S A229302 1,2,3,4,5,6,8,9,11,12,13,15,16,17,18,19,22,23,24,25,27,29,31,32,33,
%T A229302 34,36,37,38,39,41,43,44,45,46,47,48,51,53,54,58,59,61,62,64,65,66,67,
%U A229302 68,69,71,72,73,74,75,76,79,81,82,83,85,86,87,88,89,92,93
%N A229302 Numbers n such that A031971(6*n) == n (mod 6*n).
%C A229302 Complement of A229306.
%C A229302 The asymptotic density is in [0.6986, 0.7073].
%C A229302 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]
%H A229302 Jose María Grau, A. M. Oller-Marcen, and J. Sondow, <a href="http://arxiv.org/abs/1309.7941">On the congruence 1^n + 2^n +... + n^n = d (mod n), where d divides n</a>
%t A229302 g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[100], g[6*#] == # &]
%Y A229302 Cf. A014117 (numbers n such that A031971(n)==1 (mod n)).
%Y A229302 Cf. A229300 (numbers n such that A031971(1806*n)== n (mod n*1806)).
%Y A229302 Cf. A229301 (numbers n such that A031971(42*n) == n (mod 42*n)).
%Y A229302 Cf. A229302 (numbers n such that A031971(6*n) == n (mod 6*n)).
%Y A229302 Cf. A229303 (numbers n such that A031971(2*n) == n (mod 2*n)).
%Y A229302 Cf. A229304 (numbers n such that A031971(1806*n) <> n (mod n*1806)).
%Y A229302 Cf. A229305 (numbers n such that A031971(42*n) <> n (mod 42*n)).
%Y A229302 Cf. A229306 (numbers n such that A031971(6*n) <> n (mod 6*n)).
%Y A229302 Cf. A229307 (numbers n such that A031971(2*n) <> n (mod 2*n)).
%Y A229302 Cf. A229308 (primitive numbers in A229304).
%Y A229302 Cf. A229309 (primitive numbers in A229305).
%Y A229302 Cf. A229310 (primitive numbers in A229306).
%Y A229302 Cf. A229311 (primitive numbers in A229307).
%K A229302 nonn
%O A229302 1,2
%A A229302 _José María Grau Ribas_, Sep 21 2013

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