

A109067


3almost primes of the form semiprime + 1.


6



27, 50, 52, 63, 66, 70, 75, 78, 92, 116, 124, 130, 147, 170, 186, 188, 195, 207, 222, 236, 238, 255, 266, 268, 275, 279, 290, 292, 310, 322, 356, 363, 366, 387, 399, 404, 412, 418, 423, 428, 438, 452, 455, 470, 474, 483, 494, 498, 506, 518, 530, 534, 539, 555
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OFFSET

1,1


LINKS

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


FORMULA

a(n) is in this sequence iff a(n) is in A014612 and a(n)1 is in A001358.


EXAMPLE

a(1) = 27 because (2*13+1)=(3^3) = 27.
a(2) = 50 because (7*7+1)=(2*5^2) = 50.
a(3) = 52 because (3*17+1)=(2^2*13) = 52.
a(4) = 63 because (2*31+1)=(3^2*7) = 63.
a(5) = 66 because (5*13+1)=(2*3*11) = 66.
a(6) = 70 because (3*23+1)=(2*5*7) = 70.
a(7) = 75 because (2*37+1)=(3*5^2) = 75.
a(8) = 78 because (7*11+1)=(2*3*13) = 78.


MATHEMATICA

f[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[600], f[ # ] == 3 && f[ #  1] == 2 &] (* Ray Chandler, Mar 20 2007 *)
Select[Select[Range[600], PrimeOmega[#]==2&]+1, PrimeOmega[#]==3&] (* Harvey P. Dale, Nov 24 2013 *)


PROG

(PARI) list(lim)=my(v=List(), t); forprime(p=2, lim, forprime(q=2, min(p, lim\p), if(bigomega(t=p*q+1)==3, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017


CROSSREFS

Primes are in A000040. Semiprimes are in A001358. 3almost primes are in A014612.
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 this sequence.
4almost primes of the form semiprime + 1 are in A109287.
5almost primes of the form semiprime + 1 are in A109383.
Least nalmost prime of the form semiprime + 1 are in A128665.
Cf. A077065, A079148, A092307.
Sequence in context: A090761 A090760 A251143 * A034595 A102708 A154591
Adjacent sequences: A109064 A109065 A109066 * A109068 A109069 A109070


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Aug 24 2005


EXTENSIONS

Edited and extended by Ray Chandler, Mar 20 2007


STATUS

approved



