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A347243 Numbers k such that when iterating the map x -> A000593(x), we will not encounter a term x (after the starting point x=k) whose largest prime factor would be at least as large as A006530(k), before 1 is eventually reached.

%I A347243 #9 Aug 28 2021 18:20:46
%S A347243 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,26,28,29,
%T A347243 30,31,32,33,34,35,37,38,39,40,41,42,43,44,46,47,48,51,52,53,56,57,58,
%U A347243 59,60,61,62,64,65,66,67,68,69,70,71,73,74,76,77,78,79,80,82,83,84,85,86,87,88,89,91,92,93,94,95,96,97,101
%N A347243 Numbers k such that when iterating the map x -> A000593(x), we will not encounter a term x (after the starting point x=k) whose largest prime factor would be at least as large as A006530(k), before 1 is eventually reached.
%C A347243 The initial 1 is included by a convention.
%e A347243 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, which is less than the largest prime factor of 17 (which is 17 itself), thus 17 is included in this sequence.
%o A347243 (PARI)
%o A347243 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A347243 A000265(n) = (n >> valuation(n, 2));
%o A347243 A000593(n) = sigma(A000265(n));
%o A347243 A347244(n) = { my(gpf=A006530(n)); while(n>1, n = A000593(n); if(A006530(n)>=gpf,return(1))); (0); };
%o A347243 isA347243(n) = !A347244(n);
%Y A347243 Cf. A000593, A006530, A161942, A336361, A347240, A347241, A347242 (complement).
%Y A347243 Positions of zeros in A347244 and in A347245.
%Y A347243 Subsequences: A000040 (conjectured), A000079.
%K A347243 nonn
%O A347243 1,2
%A A347243 _Antti Karttunen_, Aug 28 2021