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%I #35 Dec 12 2015 00:16:42
%S 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,
%T 31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,51,53,54,56,59,
%U 61,62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,79,81
%N Numbers n such that A031971(1806*n) == n (mod 1806*n).
%C Complement of A229304.
%C The asymptotic density is in [0.7747,0.812570].
%C 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 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 g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n]; Select[Range[100], g[1806*#] == # &]
%Y Cf. A031971, A231409.
%Y Cf. A231562 (numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n)).
%Y Cf. A229312 (numbers n such that A031971(47058*n) == n (mod 47058*n)).
%Y Cf. A229300 (numbers n such that A031971(1806*n)== n (mod n*1806)).
%Y Cf. A229301 (numbers n such that A031971(42*n) == n (mod 42*n)).
%Y Cf. A229302 (numbers n such that A031971(6*n) == n (mod 6*n)).
%Y Cf. A229303 (numbers n such that A031971(2*n) == n (mod 2*n)).
%Y Cf. A229313 (numbers n such that A031971(47058*n) <> n (mod 47058*n)).
%Y Cf. A229304 (numbers n such that A031971(1806*n) <> n (mod n*1806)).
%Y Cf. A229305 (numbers n such that A031971(42*n) <> n (mod 42*n)).
%Y Cf. A229306 (numbers n such that A031971(6*n) <> n (mod 6*n)).
%Y Cf. A229307 (numbers n such that A031971(2*n) <> n (mod 2*n)).
%Y Cf. A229308 (primitive numbers in A229304).
%Y Cf. A229309 (primitive numbers in A229305).
%Y Cf. A229310 (primitive numbers in A229306).
%Y Cf. A229311 (primitive numbers in A229307).
%Y Cf. A054377 (primary pseudoperfect numbers).
%K nonn
%O 1,2
%A _José María Grau Ribas_, Sep 19 2013
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