This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229301 #22 Dec 15 2020 18:31:21
%S A229301 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 A229301 31,32,33,34,35,36,37,38,39,41,42,44,45,46,47,48,49,51,53,54,56,59,61,
%U A229301 62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,79,81,82
%N A229301 Numbers n such that A031971(42*n) == n (mod 42*n).
%C A229301 Complement of A229305.
%C A229301 The asymptotic density is in [0.7880, 0.8079].
%C A229301 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 A229301 Robert Israel, <a href="/A229301/b229301.txt">Table of n, a(n) for n = 1..1000</a>
%H A229301 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>
%p A229301 filter:= proc(n) local t,k;
%p A229301 t:= add(k &^ (42*n) mod (42*n),k=1..42*n);
%p A229301 t mod (42*n) = n
%p A229301 end proc:
%p A229301 select(filter, [$1..100]); # _Robert Israel_, Dec 15 2020
%t A229301 g[n_] := Mod[Sum[PowerMod[i, n, n], {i, n}], n];Select[Range[100], g[42*#] == # &]
%Y A229301 Cf. A014117 (numbers n such that A031971(n)==1 (mod n)).
%Y A229301 Cf. A229300 (numbers n such that A031971(1806*n)== n (mod n*1806)).
%Y A229301 Cf. A229301 (numbers n such that A031971(42*n) == n (mod 42*n)).
%Y A229301 Cf. A229302 (numbers n such that A031971(6*n) == n (mod 6*n)).
%Y A229301 Cf. A229303 (numbers n such that A031971(2*n) == n (mod 2*n)).
%Y A229301 Cf. A229304 (numbers n such that A031971(1806*n) <> n (mod n*1806)).
%Y A229301 Cf. A229305 (numbers n such that A031971(42*n) <> n (mod 42*n)).
%Y A229301 Cf. A229306 (numbers n such that A031971(6*n) <> n (mod 6*n)).
%Y A229301 Cf. A229307 (numbers n such that A031971(2*n) <> n (mod 2*n)).
%Y A229301 Cf. A229308 (primitive numbers in A229304).
%Y A229301 Cf. A229309 (primitive numbers in A229305).
%Y A229301 Cf. A229310 (primitive numbers in A229306).
%Y A229301 Cf. A229311 (primitive numbers in A229307).
%K A229301 nonn
%O A229301 1,2
%A A229301 _José María Grau Ribas_, Sep 21 2013