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The left Aurifeuillian factor of k^k + 1 for k congruent to 0, 2 or 3 (mod 4) and squarefree.
3

%I #20 Apr 29 2022 03:40:16

%S 1,1,13,113,3541,58367,2826601,19231,113631466919,9617835527609,

%T 348275601426959,35522826680397941,241498479121,

%U 8403855868042458448127,1161044975606998832441701,1272844589592126671,10128165505710094110937686497,4612290807753604561

%N The left Aurifeuillian factor of k^k + 1 for k congruent to 0, 2 or 3 (mod 4) and squarefree.

%C The values of k are given by A230375.

%C Named after the French mathematician Léon-François-Antoine Aurifeuille (1822-1882). - _Bernard Schott_, Apr 25 2022

%H Richard P. Brent, <a href="http://arxiv.org/abs/1004.5466">On computing factors of cyclotomic polynomials</a>, arXiv:1004.5466 [math.NT], 2010.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AurifeuilleanFactorization.html">Aurifeuillean Factorization</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Léon-François-Antoine_Aurifeuille">Léon-François-Antoine Aurifeuille</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aurifeuillean_factorization">Aurifeuillean factorization</a>.

%e 58367 is in the sequence because it is an Aurifeuillian factor of 11^11+1.

%Y Cf. A230375, A220983, A220984, A230375, A230376, A230378, A230379.

%K nonn

%O 1,3

%A _Colin Barker_, Oct 17 2013