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A347240 a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, but excluding the n itself. If n is a power of 2, then a(n) = 1. If 1 is never reached, then a(n) = -1.

%I A347240 #12 Feb 10 2022 20:05:44
%S A347240 1,1,2,1,3,2,2,1,13,3,3,2,7,2,3,1,13,13,5,3,2,3,3,2,31,7,5,2,5,3,2,1,
%T A347240 3,13,3,13,19,5,7,3,7,2,11,3,13,3,3,2,19,31,13,7,5,5,13,2,5,5,5,3,31,
%U A347240 2,13,1,7,3,17,13,3,3,13,13,37,19,31,5,3,7,5,3,19,7,7,2,5,11,5,3,13,13,7,3,2,3,5,2,19
%N A347240 a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, but excluding the n itself. If n is a power of 2, then a(n) = 1. If 1 is never reached, then a(n) = -1.
%H A347240 Antti Karttunen, <a href="/A347240/b347240.txt">Table of n, a(n) for n = 1..20000</a>
%F A347240 a(n) = A347241(A000593(n)). - _Antti Karttunen_, Feb 10 2022
%e A347240 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 after the initial step is 13, thus a(17) = 13.
%o A347240 (PARI)
%o A347240 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A347240 A000265(n) = (n >> valuation(n, 2));
%o A347240 A000593(n) = sigma(A000265(n));
%o A347240 A347240(n) = { my(m=1); while(n>1, n = A000593(n); m = max(m, A006530(n))); (m); };
%Y A347240 Cf. A000593, A006530, A336361, A347241, A347242, A347243, A347244.
%Y A347240 Cf. also A161942.
%K A347240 nonn
%O A347240 1,3
%A A347240 _Antti Karttunen_, Aug 28 2021