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A362178 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of omega(a(n-1)).

%I A362178 #33 Apr 13 2023 02:35:32
%S A362178 1,2,3,4,5,6,8,7,9,10,12,14,16,11,13,15,18,20,22,24,26,28,30,21,32,17,
%T A362178 19,23,25,27,29,31,33,34,36,38,40,42,39,44,46,48,50,52,54,56,58,60,45,
%U A362178 62,64,35,66,51,68,70,57,72,74,76,78,63,80,82,84,69,86,88,90,75,92,94,96,98,100
%N A362178 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of omega(a(n-1)).
%C A362178 Unlike A362077 numerous primes appear in the sequence; in the first 500000 terms there are seventy-four in total. In the same range there are twelve fixed points, the last being 57. It is unknown whether more exist.
%H A362178 Scott R. Shannon, <a href="/A362178/a362178.png">Image of the first 500000 terms</a>. The green line is a(n) = n.
%e A362178 a(5) = 5 as omega(a(4)) = A001221(4) = 1, and 5 is the smallest unused number that is a multiple of 1.
%e A362178 a(7) = 8 as omega(a(6)) = A001221(6) = 2, and 8 is the smallest unused number that is a multiple of 2.
%o A362178 (Python)
%o A362178 from itertools import count, islice
%o A362178 from sympy import primenu
%o A362178 def A362178_gen(): # generator of terms
%o A362178     a, b = {1,2}, 2
%o A362178     yield from (1,2)
%o A362178     while True:
%o A362178         for b in count(p:=primenu(b),p):
%o A362178             if b not in a:
%o A362178                 yield b
%o A362178                 a.add(b)
%o A362178                 break
%o A362178 A362178_list = list(islice(A362178_gen(),20)) # _Chai Wah Wu_, Apr 12 2023
%Y A362178 Cf. A001221, A362077, A362031, A354606, A000005, A124056, A342585.
%K A362178 nonn
%O A362178 1,2
%A A362178 _Scott R. Shannon_, Apr 11 2023