A358201 - OEIS

%I #8 Jan 16 2023 09:10:46

%S 1,2,3,4,7,6,8,5,9,13,10,12,14,15,16,31,18,20,22,24,26,28,30,32,21,27,

%T 33,34,36,35,39,38,40,25,42,44,45,46,48,50,51,52,49,54,55,56,57,58,60,

%U 62,63,64,127,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108

%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 sigma(max_{k=1..n-1}a(k)).

%C The sequence is conjectured to be a permutation of the positive integers. In the first 150000 terms the fixed points are 1, 2, 3, 4, 6, 9, 12, 93, 6003, 6881, 16269, 100707, 114839, 116999. It is likely more exist.

%H Scott R. Shannon, <a href="/A358201/a358201.png">Image of the first 150000 terms</a>. The green line is a(n) = n.

%e a(9) = 9 as sigma(max_{k=1..8}a(k)) = sigma(8) = A000203(8) = 15, and 9 is the smallest unused number that shares a factor with 15.

%Y Cf. A000203, A358176, A358082, A064413, A356851, A356430, A354960.

%K nonn,look

%O 1,2

%A _Scott R. Shannon_, Nov 03 2022