A109287 4-almost primes equal to p*q + 1, where p and q are (not necessarily distinct) primes.
16, 36, 40, 56, 88, 135, 156, 184, 204, 210, 220, 248, 250, 260, 296, 306, 315, 328, 330, 340, 342, 372, 414, 459, 472, 490, 516, 536, 546, 580, 584, 636, 650, 686, 690, 708, 714, 732, 735, 738, 804, 808, 819, 836, 850, 852, 870, 872, 940, 950, 966, 975, 996
Offset: 1
Examples
a(1) = 16 because (3*5+1)=(2^4) = 16. a(2) = 36 because (5*7+1)=((2^2)*(3^2)) = 36. a(3) = 40 because (3*13+1)=((2^3)*5) = 40. a(4) = 56 because (5*11+1)=((2^3)*7) = 56. a(5) = 88 because (3*29+1)=((2^3)*11) = 88. a(6) = 135 because (2*67+1)=((3^3)*5) = 135. a(7) = 156 because (5*31+1)=((2^2)*3*13) = 156. a(8) = 184 because (3*61+1)=((2^3)*23) = 184.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Crossrefs
Primes of the form semiprime + 1 are in A005385 (safe primes).
Semiprimes of the form semiprime + 1 are in A109373.
3-almost primes of the form semiprime + 1 are in A109067.
4-almost primes of the form semiprime + 1 are in this sequence.
5-almost primes of the form semiprime + 1 are in A109383.
Least n-almost prime of the form semiprime + 1 are in A128665.
Programs
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Mathematica
bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1000], bo[ # ] == 4 && bo[ # - 1] == 2 &] (* Ray Chandler, Aug 27 2005 *)
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PARI
is(n)=bigomega(n)==4 && bigomega(n-1)==2 \\ Charles R Greathouse IV, Sep 16 2015
Extensions
Extended by Ray Chandler, Aug 27 2005
Edited by Ray Chandler, Mar 20 2007
Comments