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A279188 Maximal entry in row c of triangle in A279185, where c = prime(n)^2 = A001248(n).

%I A279188 #27 Dec 26 2019 12:53:43
%S A279188 1,2,4,6,20,12,8,18,110,84,20,36,20,42,253,156,812,60,330,420,18,156,
%T A279188 820,110,48,100,408,2756,36,84,42,780,136,1518,1332,60,156,162,6806,
%U A279188 1204,1958,180,3420,96,588,990,420,1332,3164,684,812,2856,24,100
%N A279188 Maximal entry in row c of triangle in A279185, where c = prime(n)^2 = A001248(n).
%C A279188 Needs to be checked (there are really two sequences that should be included: the maximal entry in row c, and the LCM of the entries in row c).
%H A279188 Vincenzo Librandi, <a href="/A279188/b279188.txt">Table of n, a(n) for n = 1..200</a>
%H A279188 Haifeng Xu, <a href="http://arxiv.org/abs/1601.06509">The largest cycles consist by the quadratic residues and Fermat primes</a>, arXiv:1601.06509 [math.NT], 2016.
%p A279188 A279188 := proc(n)
%p A279188     A279186(ithprime(n)^2) ;
%p A279188 end proc :
%p A279188 seq(A279188(n),n=1..80) ; # _R. J. Mathar_, Dec 15 2016
%t A279188 T[n_, k_] := Module[{g, y, r}, If[k == 0, Return[1]]; y = n; g = GCD[k, y]; While[g > 1, y = y/g; g = GCD[k, y]]; If[y == 1, Return[1]]; r = MultiplicativeOrder[k, y]; r = r/2^IntegerExponent[r, 2]; If[r == 1, Return[1]]; MultiplicativeOrder[2, r]];
%t A279188 a[n_] := a[n] = With[{c = Prime[n]^2}, Table[T[c, k], {k, 0, c-1}] // Max];
%t A279188 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 54}] (* _Jean-François Alcover_, Nov 27 2017, after _Robert Israel_ *)
%Y A279188 Cf. A001248, A279185.
%K A279188 nonn
%O A279188 1,2
%A A279188 _N. J. A. Sloane_, Dec 14 2016