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A332768 a(n) is the greatest prime factor of A180045(n).

%I A332768 #10 Feb 24 2020 14:25:19
%S A332768 7,5,13,11,13,3,13,5,7,19,17,7,11,19,31,5,11,29,19,23,7,3,11,13,11,7,
%T A332768 31,43,41,37,7,31,17,17,29,7,41,23,19,37,31,19,19,5,11,7,17,31,7,13,
%U A332768 29,5,43,31,61,7,41,37,73,23,53,31,13,71,23,11,61,67,11
%N A332768 a(n) is the greatest prime factor of A180045(n).
%C A332768 Corvaja and Zannier showed that a(n) tends to infinity as n tends to infinity.
%H A332768 Rémy Sigrist, <a href="/A332768/b332768.txt">Table of n, a(n) for n = 1..10000</a>
%H A332768 P. Corvaja and U. Zannier, <a href="https://arxiv.org/abs/math/0205136">On the greatest prime factor of (ab+1)(ac+1)</a>, arXiv:math/0205136 [math.NT], 2002.
%H A332768 Rémy Sigrist, <a href="/A332768/a332768.gp.txt">PARI program for A332768</a>
%F A332768 a(n) = A006530(A180045(n)).
%e A332768 The first terms, alongside A180045(n), are:
%e A332768   n   a(n)  A180045(n)
%e A332768   --  ----  --------------
%e A332768    1     7   28 =  7 * 2^2
%e A332768    2     5   45 =  5 * 3^2
%e A332768    3    13   65 = 13 * 5
%e A332768    4    11   66 = 11 * 3 * 2
%e A332768    5    13   91 = 13 * 7
%e A332768    6     3   96 =  3 * 2^5
%e A332768    7    13  117 = 13 * 3^2
%e A332768    8     5  120 =  5 * 3 * 2^3
%e A332768    9     7  126 =  7 * 3^2 * 2
%e A332768   10    19  133 = 19 * 7
%o A332768 (PARI) See Links section.
%Y A332768 Cf. A006530, A180045, A260234.
%K A332768 nonn,look
%O A332768 1,1
%A A332768 _Rémy Sigrist_, Feb 23 2020