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A354160 Products of exactly two distinct primes in A090252, in order of appearance.

%I A354160 #15 Jun 17 2022 03:24:18
%S A354160 21,55,26,85,57,161,319,217,481,205,731,517,159,1121,1403,871,355,
%T A354160 1241,869,2407,1691,413,3007,2323,206,1391,4033,565,5207,2227,5891,
%U A354160 6533,4321,453,1007,623,4867,2231,6161,2119,11189,6401,12709,7421,2159,9563,8213,1507,15247,9259,4031,12367,597,2869,11183,1561,13393,7099,3611,14213,478,24823
%N A354160 Products of exactly two distinct primes in A090252, in order of appearance.
%H A354160 Michael De Vlieger, <a href="/A354160/b354160.txt">Table of n, a(n) for n = 1..2517</a>
%H A354160 Michael De Vlieger, <a href="/A354160/a354160.png">Annotated log-log scatterplot of A090252(n)</a>, n = 1..2^12, labeling primes in red, highlighting composite prime powers in gold, squarefree semiprimes in green and labeling them in boldface.
%t A354160 Select[Import["https://oeis.org/A090252/b090252.txt", "Data"][[1 ;; 2000, -1]], PrimeNu[#] == PrimeOmega[#] == 2 &] (* _Michael De Vlieger_, Jun 16 2022 *)
%o A354160 (Python)
%o A354160 from itertools import count, islice
%o A354160 from collections import deque
%o A354160 from math import gcd, lcm
%o A354160 from sympy import factorint
%o A354160 def A354160_gen(): # generator of terms
%o A354160     aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
%o A354160     while True:
%o A354160         for m in count(c):
%o A354160             if m not in aset and gcd(m,b) == 1:
%o A354160                 if len(fm := factorint(m)) == sum(fm.values()) == 2:
%o A354160                     yield m
%o A354160                 aset.add(m)
%o A354160                 aqueue.append(m)
%o A354160                 if f: aqueue.popleft()
%o A354160                 b = lcm(*aqueue)
%o A354160                 f = not f
%o A354160                 while c in aset:
%o A354160                     c += 1
%o A354160                 break
%o A354160 A354160_list = list(islice(A354160_gen(),25)) # _Chai Wah Wu_, May 31 2022
%Y A354160 Cf. A090252, A354159, A354161, A354162, A354163.
%K A354160 nonn
%O A354160 1,1
%A A354160 _N. J. A. Sloane_, May 30 2022