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A365059 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).

%I A365059 #9 Sep 18 2023 09:01:35
%S A365059 2,4,6,5,10,7,14,9,3,12,15,8,16,18,20,21,30,40,28,27,24,25,35,36,45,
%T A365059 32,22,13,26,60,50,42,48,55,64,34,19,38,63,70,56,54,65,72,75,80,49,77,
%U A365059 90,100,84,96,85,44,39,112,81,33,98,99,126,108,95,120,110,144,105,135,88,52,150,130,140
%N A365059 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).
%C A365059 In the first 500000 terms the only fixed points are 38 and 209, although it is likely more exist. In the same range the smallest missing numbers are 311, 313, 337. The sequence is conjectured to be a permutation of the integers >= 2.
%H A365059 Scott R. Shannon, <a href="/A365059/b365059.txt">Table of n, a(n) for n = 1..10000</a>
%H A365059 Scott R. Shannon, <a href="/A365059/a365059.png">Image of the first 500000 terms</a>. The green line is a(n) = n.
%e A365059 a(3) = 6 as a(2) = 4 and A008472(4) = 2, and 6 is the smallest unused number that is a multiple of 2.
%e A365059 a(11) = 15 as a(10) = 12 and A008472(12) = 5, and 15 is the smallest unused number that is a multiple of 5.
%Y A365059 Cf. A008472, A365060, A300813.
%K A365059 nonn
%O A365059 1,1
%A A365059 _Scott R. Shannon_, Aug 19 2023