|
%I #18 Dec 11 2015 22:05:36
%S 7,10,14,20,21,26,28,30,35,40,42,49,50,52,55,56,57,60,63,70,77,78,80,
%T 84,90,91,98,100,104,105,110,112,114,119,120,126,130,133,136,140,147,
%U 150,154,155,156,160,161,165,168,170,171,175,180,182,189,190,196
%N Numbers n such that A031971(6*n) <> n (mod 6*n)
%C Complement of A229302.
%C The asymptotic density is in [0.2927, 0.3014].
%C If n is in A then k*n is in A for all natural number k.
%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[6*#] == # &]
%Y Cf. A014117 (numbers n such that A031971(n)==1 (mod 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. 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).
%K nonn
%O 1,1
%A _José María Grau Ribas_, Sep 24 2013
|
