OFFSET
1,1
COMMENTS
k is a member if (1) k = p*q p, q are primes; (2) k = 4*p and p, 2p+1 are primes. Are there any other prime signatures k could take?
The odd members (A046315) outnumber the even members. - Robert G. Wilson v, Mar 31 2005
This sequence consists of precisely the semiprimes and numbers of the form 4p where 2p+1 is also prime. n cannot have pq as a proper divisor, with p and q odd primes (not necessarily distinct). Likewise 8 cannot be a proper factor. This eliminates all but the specified cases. - Franklin T. Adams-Watters, Jul 28 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..7000
MATHEMATICA
fQ[n_] := Block[{d = Take[ Divisors[n], {2, -2}]}, Union[ Flatten[ PrimeQ[{Select[d, OddQ[ # ] &], Select[d, EvenQ[ # ] &] + 1}]]] == {True}]; Select[ Range[ 176], fQ[ # ] &] (* Robert G. Wilson v, Mar 31 2005 *)
cnQ[n_]:=Module[{d=Most[Rest[Divisors[n]]]}, AllTrue[Join[Select[ d, OddQ], Select[ d, EvenQ]+1], PrimeQ]]; Select[Range[200], CompositeQ[#] && cnQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 05 2019 *)
PROG
(PARI) is(n)=fordiv(n, d, if(!isprime(bitor(d, 1)) && d>1, return(d==n))); !isprime(n) && n>1 \\ Charles R Greathouse IV, Sep 24 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 29 2002
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Mar 31 2005
Definition corrected, following an observation by Franklin T. Adams-Watters. - Charles R Greathouse IV, Sep 24 2012
STATUS
approved