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%I #12 Sep 04 2020 08:54:13
%S 3,7,13,31,73,127,307,331,757
%N Primes p such that the Wendt determinant A048954(p) has prime factors less than p.
%C Michael B Rees has conjectured that for all primes p, each fully exponentiated prime factor less than p that divides the Wendt determinant W(p), if it exists, is of the form k*p + 1.
%C This sequence identifies the prime index p of Wendt determinants W(p) that have prime factors less than p.
%C These prime indices appear to be a subset of the lucky primes A031157.
%H Gerard P. Michon, <a href="http://www.numericana.com/data/wendt.htm">Factorization of Wendt's Determinant</a> (table for n=1 to 114).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant matrix</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%e a(3) = 13. The Wendt determinant with a prime index p = 13 has prime factors less than p. W(13) = 3^6*53^2*79^2*131^2*521^2*8191 and 3^6 = 729 is of the form k*13 + 1. It is the 3rd occurrence of such a determinant.
%t w[n_] := Resultant[x^n-1, (1+x)^n-1, x]; getp[n_] := Module[{W=w[n], lst=Table[Prime[m], {m, 1, PrimePi[n]}], lst1={}, j, k, l}, Do[j=1; While[W>0&&IntegerQ[W/lst[[l]]^j], j++]; If[j-1>0, AppendTo[lst1, {lst[[l]], j-1}]], {l, 1, Length@lst}]; Join[{n}, lst1]]; lst = {}; Do[lst1=getp[Prime[n]]; If[Length@lst1>1, AppendTo[lst, lst1[[1]]]], {n, 1, PrimePi[331]}]; lst
%Y Cf. A048954, A336280.
%K nonn,more
%O 1,1
%A _Frank M Jackson_ and Michael B Rees, Jul 31 2020
%E a(9) from _Jinyuan Wang_, Sep 04 2020
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