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A362077 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 A362077 #18 Aug 28 2023 08:21:24
%S A362077 1,2,3,4,6,8,9,10,12,15,14,16,20,18,21,22,24,28,27,30,33,26,32,5,7,11,
%T A362077 13,17,19,23,25,34,36,40,44,39,38,42,45,48,35,46,50,51,52,54,56,60,64,
%U A362077 66,57,58,62,68,63,69,70,72,55,74,76,75,78,81,80,65,82,84,88,92,87,86,90,96,102,93
%N A362077 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 A362077 Other than the first three terms the only other primes in the first 500000 terms are the consecutive terms a(24)..a(30) = 5, 7, 11, 13, 17, 19, 23. It is unknown if more exist.
%C A362077 In the same range the fixed points are 1, 2, 3, 4, and 48559, although it is possible more exist.
%H A362077 Scott R. Shannon, <a href="/A362077/b362077.txt">Table of n, a(n) for n = 1..10000</a>
%H A362077 Scott R. Shannon, <a href="/A362077/a362077.png">Image of the first 200000 terms</a>. The green line is a(n) = n.
%e A362077 a(4) = 4 as Omega(a(3)) = A001222(3) = 1, and 4 is the smallest unused number that is a multiple of 1.
%e A362077 a(10) = 15 as Omega(a(9)) = A001222(12) = 3, and 15 is the smallest unused number that is a multiple of 3.
%o A362077 (Python)
%o A362077 from sympy import primeomega
%o A362077 from itertools import count, islice
%o A362077 def A362077_gen(): # generator of terms
%o A362077     a, b = {1,2}, 2
%o A362077     yield from (1,2)
%o A362077     while True:
%o A362077         for b in count(p:=primeomega(b),p):
%o A362077             if b not in a:
%o A362077                 yield b
%o A362077                 a.add(b)
%o A362077                 break
%o A362077 A362077_list = list(islice(A362077_gen(),20)) # _Chai Wah Wu_, Apr 11 2023
%Y A362077 Cf. A001222, A362031, A354606, A000005, A124056, A342585.
%K A362077 nonn
%O A362077 1,2
%A A362077 _Scott R. Shannon_, Apr 08 2023