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%I #11 Jan 16 2023 09:10:46
%S 1,2,4,6,3,7,9,41,8,12,15,11,127,18,5,14,10,16,277,21,24,28,22,431,
%T 491,20,26,30,25,23,27,32,857,35,42,19,33,34,13,36,38,40,37,39,44,45,
%U 46,43,48,1987,50,52,51,54,56,57,58,60,49,62,55,64,61,63,82,66,3631,69,17,72,65,70,68,74
%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 A024916(n-1) = Sum_{k=1..n-1} sigma(k).
%C The majority of terms are concentrated just below the line a(n) = n. However, some terms are much larger because the sum of the divisors of all previous terms is a prime number. In the first 5000 terms there are thirteen fixed points: 32, 52, 54, ..., 1331, 2082, 2097.
%C Conjecture: the sequence is a permutation of the positive integers.
%H Scott R. Shannon, <a href="/A358209/a358209.png">Image of the first 5000 terms where a(n) is less than 110% of n</a>. The green line is a(n) = n.
%e a(5) = 3 as sigma(1) + sigma(2) + sigma(3) + sigma(4) = A024916(4) = 15, and 3 is the smallest unused number that shares a factor with 15.
%Y Cf. A358208, A024916, A000203, A356851, A064413.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Nov 04 2022