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A109067 3-almost primes of the form semiprime + 1. 6

%I #15 Oct 13 2019 09:49:39

%S 27,50,52,63,66,70,75,78,92,116,124,130,147,170,186,188,195,207,222,

%T 236,238,255,266,268,275,279,290,292,310,322,356,363,366,387,399,404,

%U 412,418,423,428,438,452,455,470,474,483,494,498,506,518,530,534,539,555

%N 3-almost primes of the form semiprime + 1.

%H Vincenzo Librandi, <a href="/A109067/b109067.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) is in this sequence iff a(n) is in A014612 and a(n)-1 is in A001358.

%e a(1) = 27 because (2*13+1)=(3^3) = 27.

%e a(2) = 50 because (7*7+1)=(2*5^2) = 50.

%e a(3) = 52 because (3*17+1)=(2^2*13) = 52.

%e a(4) = 63 because (2*31+1)=(3^2*7) = 63.

%e a(5) = 66 because (5*13+1)=(2*3*11) = 66.

%e a(6) = 70 because (3*23+1)=(2*5*7) = 70.

%e a(7) = 75 because (2*37+1)=(3*5^2) = 75.

%e a(8) = 78 because (7*11+1)=(2*3*13) = 78.

%t f[n_] := Plus @@ Last /@ FactorInteger[n];Select[Range[600], f[ # ] == 3 && f[ # - 1] == 2 &] (* _Ray Chandler_, Mar 20 2007 *)

%t Select[Select[Range[600],PrimeOmega[#]==2&]+1,PrimeOmega[#]==3&] (* _Harvey P. Dale_, Nov 24 2013 *)

%o (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 Primes are in A000040. Semiprimes are in A001358. 3-almost primes are in A014612.

%Y Primes of the form semiprime + 1 are in A005385 (safe primes).

%Y Semiprimes of the form semiprime + 1 are in A109373.

%Y 3-almost primes of the form semiprime + 1 are in this sequence.

%Y 4-almost primes of the form semiprime + 1 are in A109287.

%Y 5-almost primes of the form semiprime + 1 are in A109383.

%Y Least n-almost prime of the form semiprime + 1 are in A128665.

%Y Cf. A077065, A079148, A092307.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 24 2005

%E Edited and extended by _Ray Chandler_, Mar 20 2007

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)