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A362811 Sphenic numbers (product of 3 distinct primes) sandwiched between two semiprimes (product of 2 primes).

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%I A362811 #21 Jun 15 2023 10:35:53
%S A362811 186,266,290,322,470,518,534,582,590,670,754,790,814,894,994,1146,
%T A362811 1158,1166,1338,1370,1390,1562,1686,1798,1842,1958,2118,2158,2230,
%U A362811 2318,2454,2482,2514,2570,2630,2758,2786,2810,2922,2930,2994,3154,3206,3262,3278,3378,3454,3522,3562
%N A362811 Sphenic numbers (product of 3 distinct primes) sandwiched between two semiprimes (product of 2 primes).
%C A362811 Every term k is even. Otherwise one of k-1 or k+1 would be a multiple of 4, hence not a semiprime.
%H A362811 Michael De Vlieger, <a href="/A362811/b362811.txt">Table of n, a(n) for n = 1..10000</a>
%e A362811 186 is a term because 186=2*3*31, 185=5*37, 187=11*17.
%t A362811 Select[Range[2, 3600, 2], FactorInteger[#][[;; , 2]] == {1, 1, 1} && PrimeOmega[# - 1] == 2 && PrimeOmega[# + 1] == 2 &] (* _Amiram Eldar_, May 05 2023 *)
%o A362811 (PARI) isok(k)=omega(k)==3 && bigomega(k)==3 && bigomega(k-1)==2 && bigomega(k+1)==2
%Y A362811 Cf. A007304, A001358, A171179.
%K A362811 nonn,easy
%O A362811 1,1
%A A362811 _Alexandru Petrescu_, May 04 2023