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A279187 Maximal entry in row c of A279185, where c = n-th composite number A002808(n).

%I A279187 #18 Nov 27 2017 09:21:31
%S A279187 1,1,1,2,1,1,2,1,1,2,1,2,4,1,4,2,6,2,1,1,4,1,2,2,6,2,1,2,4,2,10,1,6,4,
%T A279187 1,2,6,4,2,6,3,1,4,2,1,2,4,1,10,2,2,6,4,6,4,2,1,18,4,2,1,6,3,4,2,2,10,
%U A279187 4,11,6,1,6,4,4,1,2,2,12,6,4,6,2,6,10,3,2
%N A279187 Maximal entry in row c of A279185, where c = n-th composite number A002808(n).
%C A279187 There are really two sequences that should be included if missing: the maximal entry in row c, and the LCM of the entries in row c.
%C A279187 a(n) and the LCM variant A256608(A002808(n)) are equal at least up to n<=1100. - _R. J. Mathar_, Dec 15 2016
%H A279187 R. J. Mathar, <a href="/A279187/b279187.txt">Table of n, a(n) for n = 1..1000</a>
%H A279187 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 A279187 A279187 := proc(n)
%p A279187     A279186(A002808(n)) ;
%p A279187 end proc :
%p A279187 seq(A279187(n),n=1..180) ; # _R. J. Mathar_, Dec 15 2016
%t A279187 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]]; Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];
%t A279187 a[n_] := a[n] = With[{c = Composite[n]}, Table[T[c, k], {k, 0, c-1}] // Max ];
%t A279187 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 86}] (* _Jean-François Alcover_, Nov 27 2017, after _Robert Israel_ *)
%Y A279187 Cf. A002808, A256608 (lcm of entries in row n), A279185, A279186 (max entry in row n).
%K A279187 nonn
%O A279187 1,4
%A A279187 _N. J. A. Sloane_, Dec 14 2016