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A231233 Triangle T(n,k) = greatest prime factor of n*k+1.

%I A231233 #24 Sep 23 2018 22:29:09
%S A231233 2,3,5,2,7,5,5,3,13,17,3,11,2,7,13,7,13,19,5,31,37,2,5,11,29,3,43,5,3,
%T A231233 17,5,11,41,7,19,13,5,19,7,37,23,11,2,73,41,11,7,31,41,17,61,71,3,13,
%U A231233 101,3,23,17,5,7,67,13,89,5,37,61,13,5,37,7,61,73,17,97,109,11,19,29
%N A231233 Triangle T(n,k) = greatest prime factor of n*k+1.
%H A231233 Michel Marcus, <a href="/A231233/b231233.txt">Rows n = 1..100 of triangle, flattened</a>
%H A231233 Étienne Fouvry, <a href="http://arxiv.org/abs/1311.1161">On the greatest prime factor of ab+1</a>, arXiv:1311.1161 [math.NT], 2013.
%F A231233 T(n, k) = A006530(n*k+1).
%e A231233 Triangle begins:
%e A231233   2;
%e A231233   3,  5;
%e A231233   2,  7,  5;
%e A231233   5,  3, 13, 17;
%e A231233   3, 11,  2,  7, 13;
%e A231233   7, 13, 19,  5, 31, 37;
%e A231233   2,  5, 11, 29,  3, 43,  5;
%t A231233 T[n_, k_] := FactorInteger[n k + 1][[-1, 1]];
%t A231233 Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 23 2018 *)
%o A231233 (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, f = factor(n*k+1); print1(f[#f~, 1], ", ");); print(););}
%o A231233 (GAP) Flat(List([1..12],n->List([1..n],k->Maximum(FactorsInt(n*k+1))))); # _Muniru A Asiru_, Sep 23 2018
%Y A231233 Cf. A005408, A016777, A016813, A016861, A016921, A016993, A017077, A017173.
%K A231233 nonn,tabl
%O A231233 1,1
%A A231233 _Michel Marcus_, Nov 06 2013