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%I #11 Mar 12 2015 20:10:16
%S 39607528021345872635,118822584064037617905,198037640106729363175,
%T 356467752192112853715,435682808234804598985,514897864277496344255,
%U 594112920320188089525,673327976362879834795,752543032405571580065,910973144490955070605,990188200533646815875
%N Numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n).
%C The number 8490421583559688410706771261086 occurring in the name is the 8th term of A230311.
%C The numbers in A230311 are the values of k such that the set {n : A031971(k*n)== n (mod k*n)} is nonempty.
%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 fa = FactorInteger; Car[k_, n_] := Mod[n - Sum[If[IntegerQ[k/(fa[n][[i, 1]] - 1)], n/fa[n][[i,1]], 0], {i, 1, Length[fa[n]]}], n]; supercar[k_, n_] := If[k == 1 || Mod[k, 2] == 0 || Mod[n, 4] > 0, Car[k, n], Mod[Car[k, n] - n/2,]]; Select[39607528021345872635*Range[15],supercar[8490421583559688410706771261086*#, 8490421583559688410706771261086*#] == # &]
%Y Cf. A031971, A230311.
%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).
%K nonn
%O 1,1
%A _José María Grau Ribas_, Nov 16 2013
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