

A109287


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


9



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
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OFFSET

1,1


COMMENTS

4almost 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 &] (*Chandler*)


PROG

(PARI) is(n)=bigomega(n)==4 && bigomega(n1)==2 \\ Charles R Greathouse IV, Sep 16 2015


CROSSREFS

Primes are in A000040. Semiprimes are in A001358. 4almost primes are in A014613.
Primes of the form semiprime + 1 are in A005385 (safe primes).
Semiprimes of the form semiprime + 1 are in A109373.
3almost primes of the form semiprime + 1 are in A109067.
4almost primes of the form semiprime + 1 are in this sequence.
5almost primes of the form semiprime + 1 are in A109383.
Least nalmost 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 A066112 A223456
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



