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A347241 a(1) = 1, and for n > 1, a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, and including the n itself. If 1 is never reached when starting from n, then a(n) = -1.

%I A347241 #8 Feb 10 2022 20:05:57
%S A347241 1,2,3,2,5,3,7,2,13,5,11,3,13,7,5,2,17,13,19,5,7,11,23,3,31,13,5,7,29,
%T A347241 5,31,2,11,17,7,13,37,19,13,5,41,7,43,11,13,23,47,3,19,31,17,13,53,5,
%U A347241 13,7,19,29,59,5,61,31,13,2,13,11,67,17,23,7,71,13,73,37,31,19,11,13,79,5,19,41,83,7,17,43,29
%N A347241 a(1) = 1, and for n > 1, a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, and including the n itself. If 1 is never reached when starting from n, then a(n) = -1.
%H A347241 Antti Karttunen, <a href="/A347241/b347241.txt">Table of n, a(n) for n = 1..20000</a>
%F A347241 a(n) = max(A006530(n), A347240(n)).
%e A347241 For n = 17, the iteration proceeds as follows 17 -> 18 (= 2*3*3), 18 -> 13 (13 is a prime), 13 -> 14 (= 2*7), 14 -> 8 (= 2*2*2), 8 -> 1. The largest prime factor present (when including the starting term also) is 17, thus a(17) = 17.
%o A347241 (PARI)
%o A347241 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A347241 A000265(n) = (n >> valuation(n, 2));
%o A347241 A000593(n) = sigma(A000265(n));
%o A347241 A347241(n) = { my(m=1); while(n>1, m = max(m, A006530(n)); n = A000593(n)); (m); };
%Y A347241 Cf. A000593, A006530, A161942, A336361, A347240, A347242.
%K A347241 nonn
%O A347241 1,2
%A A347241 _Antti Karttunen_, Aug 28 2021