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

1,1

Comments

4-almost primes of the form semiprime + 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

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

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A070588 A250432 A183196 * A294155 A330869 A334538

Adjacent sequences: A109284 A109285 A109286 * A109288 A109289 A109290

Keyword

easy,nonn

Author

Giovanni Teofilatto and Jonathan Vos Post, Aug 20 2005

Extensions

Extended by Ray Chandler, Aug 27 2005

Edited by Ray Chandler, Mar 20 2007

Status

approved