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%I #11 Aug 31 2022 13:32:04
%S 1,2,4,3,18,7,11,76,322,29,1364,123,47,199,24476,843,5778,521
%N a(n) is the new Lucas divisor that appears at the step A356062(n).
%C The sequence is not monotonic.
%C Conjecture: the sequence is well defined, i.e., it is not possible that two new Lucas divisors arrive while one disappears for some step in A356062.
%e a(1) = 1 because the smallest integer that has only one Lucas divisor is 1 since 1 is the smallest Lucas number in A000032.
%e A356062(6) = 252 and the set of the six Lucas divisors of 252 is {1, 2, 3, 4, 7, 18}. Then, A356062(7) = 2772 and the set of the seven Lucas divisors of 2772 is {1, 2, 3, 4, 7, 11, 18}. The new Lucas divisor that appears in this set is 11, hence a(7) = 11.
%Y Cf. A000032, A304092, A349100, A356062.
%K nonn,more
%O 1,2
%A _Bernard Schott_, Jul 25 2022