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A109067 3-almost primes of the form semiprime + 1.

%I A109067 #15 Oct 13 2019 09:49:39
%S A109067 27,50,52,63,66,70,75,78,92,116,124,130,147,170,186,188,195,207,222,
%T A109067 236,238,255,266,268,275,279,290,292,310,322,356,363,366,387,399,404,
%U A109067 412,418,423,428,438,452,455,470,474,483,494,498,506,518,530,534,539,555
%N A109067 3-almost primes of the form semiprime + 1.
%H A109067 Vincenzo Librandi, <a href="/A109067/b109067.txt">Table of n, a(n) for n = 1..1000</a>
%F A109067 a(n) is in this sequence iff a(n) is in A014612 and a(n)-1 is in A001358.
%e A109067 a(1) = 27 because (2*13+1)=(3^3) = 27.
%e A109067 a(2) = 50 because (7*7+1)=(2*5^2) = 50.
%e A109067 a(3) = 52 because (3*17+1)=(2^2*13) = 52.
%e A109067 a(4) = 63 because (2*31+1)=(3^2*7) = 63.
%e A109067 a(5) = 66 because (5*13+1)=(2*3*11) = 66.
%e A109067 a(6) = 70 because (3*23+1)=(2*5*7) = 70.
%e A109067 a(7) = 75 because (2*37+1)=(3*5^2) = 75.
%e A109067 a(8) = 78 because (7*11+1)=(2*3*13) = 78.
%t A109067 f[n_] := Plus @@ Last /@ FactorInteger[n];Select[Range[600], f[ # ] == 3 && f[ # - 1] == 2 &] (* _Ray Chandler_, Mar 20 2007 *)
%t A109067 Select[Select[Range[600],PrimeOmega[#]==2&]+1,PrimeOmega[#]==3&] (* _Harvey P. Dale_, Nov 24 2013 *)
%o A109067 (PARI) list(lim)=my(v=List(),t); forprime(p=2,lim, forprime(q=2,min(p,lim\p), if(bigomega(t=p*q+1)==3, listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017
%Y A109067 Primes are in A000040. Semiprimes are in A001358. 3-almost primes are in A014612.
%Y A109067 Primes of the form semiprime + 1 are in A005385 (safe primes).
%Y A109067 Semiprimes of the form semiprime + 1 are in A109373.
%Y A109067 3-almost primes of the form semiprime + 1 are in this sequence.
%Y A109067 4-almost primes of the form semiprime + 1 are in A109287.
%Y A109067 5-almost primes of the form semiprime + 1 are in A109383.
%Y A109067 Least n-almost prime of the form semiprime + 1 are in A128665.
%Y A109067 Cf. A077065, A079148, A092307.
%K A109067 easy,nonn
%O A109067 1,1
%A A109067 _Jonathan Vos Post_, Aug 24 2005
%E A109067 Edited and extended by _Ray Chandler_, Mar 20 2007