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%I #34 Jan 16 2023 09:10:46
%S 1,2,4,11,23,47,5,101,7,211,3,14,22,487,6,9,8,10,1033,12,15,13,18,16,
%T 2203,21,46,26,29,4583,89,9257,20,28,35,18661,24,17,27,37441,30,19,25,
%U 32,33,36,34,38,39,40,42,44,45,48,37,31,50,49,52,54,56,58,60,62,63,51,57,64,55,66,69,72
%N a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} sigma(a(k)).
%C The sequence shows large jumps in value due to the sum occasionally forming a large prime, e.g., a(279) = 2650277753. The sequence is conjectured to be a permutation of the positive integers.
%e a(7) = 5 as Sum_{k=1..6} sigma(a(k)) = Sum_{k=1..6} A000203(a(k)) = 1 + 3 + 7 + 12 + 24 + 48 = 95, and 5 is the smallest unused number that shares a factor with 95.
%Y Cf. A000203, A358176, A358201, A064413, A356851, A356430, A354960.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Nov 02 2022