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

Author

Giovanni Teofilatto and Jonathan Vos Post, Aug 20 2005

Keywords

• easy
• nonn

Comments

4-almost primes of the form semiprime + 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 are in A000040. Semiprimes are in A001358. 4-almost primes are in A014613.

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.

Similar to A076153; after A076153(0)=3 next difference is A076153(100)=1792 whereas A109287(100)=1794.

Cf. A077065, A079148, A092307, A109288, A109289, A109290.

Programs

Mathematica

bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1000], bo[ # ] == 4 && bo[ # - 1] == 2 &] (* Ray Chandler, Aug 27 2005 *)

PARI

is(n)=bigomega(n)==4 && bigomega(n-1)==2 \\ Charles R Greathouse IV, Sep 16 2015

Formula

a(n) is in this sequence iff a(n) is in A014613 and (a(n)-1) is in A001358.

Extensions

Extended by Ray Chandler, Aug 27 2005

Edited by Ray Chandler, Mar 20 2007