cp's OEIS Frontend

A109287 4-almost primes equal to p*q + 1, where p and q are (not necessarily distinct) primes.

%I A109287 #14 Oct 13 2019 09:47:37
%S A109287 16,36,40,56,88,135,156,184,204,210,220,248,250,260,296,306,315,328,
%T A109287 330,340,342,372,414,459,472,490,516,536,546,580,584,636,650,686,690,
%U A109287 708,714,732,735,738,804,808,819,836,850,852,870,872,940,950,966,975,996
%N A109287 4-almost primes equal to p*q + 1, where p and q are (not necessarily distinct) primes.
%C A109287 4-almost primes of the form semiprime + 1.
%H A109287 Vincenzo Librandi, <a href="/A109287/b109287.txt">Table of n, a(n) for n = 1..1000</a>
%F A109287 a(n) is in this sequence iff a(n) is in A014613 and (a(n)-1) is in A001358.
%e A109287 a(1) = 16 because (3*5+1)=(2^4) = 16.
%e A109287 a(2) = 36 because (5*7+1)=((2^2)*(3^2)) = 36.
%e A109287 a(3) = 40 because (3*13+1)=((2^3)*5) = 40.
%e A109287 a(4) = 56 because (5*11+1)=((2^3)*7) = 56.
%e A109287 a(5) = 88 because (3*29+1)=((2^3)*11) = 88.
%e A109287 a(6) = 135 because (2*67+1)=((3^3)*5) = 135.
%e A109287 a(7) = 156 because (5*31+1)=((2^2)*3*13) = 156.
%e A109287 a(8) = 184 because (3*61+1)=((2^3)*23) = 184.
%t A109287 bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1000], bo[ # ] == 4 && bo[ # - 1] == 2 &] (* _Ray Chandler_, Aug 27 2005 *)
%o A109287 (PARI) is(n)=bigomega(n)==4 && bigomega(n-1)==2 \\ _Charles R Greathouse IV_, Sep 16 2015
%Y A109287 Primes are in A000040. Semiprimes are in A001358. 4-almost primes are in A014613.
%Y A109287 Primes of the form semiprime + 1 are in A005385 (safe primes).
%Y A109287 Semiprimes of the form semiprime + 1 are in A109373.
%Y A109287 3-almost primes of the form semiprime + 1 are in A109067.
%Y A109287 4-almost primes of the form semiprime + 1 are in this sequence.
%Y A109287 5-almost primes of the form semiprime + 1 are in A109383.
%Y A109287 Least n-almost prime of the form semiprime + 1 are in A128665.
%Y A109287 Similar to A076153; after A076153(0)=3 next difference is A076153(100)=1792 whereas A109287(100)=1794.
%Y A109287 Cf. A077065, A079148, A092307, A109288, A109289, A109290.
%K A109287 easy,nonn
%O A109287 1,1
%A A109287 _Giovanni Teofilatto_ and _Jonathan Vos Post_, Aug 20 2005
%E A109287 Extended by _Ray Chandler_, Aug 27 2005
%E A109287 Edited by _Ray Chandler_, Mar 20 2007