%I #21 Mar 23 2018 04:02:41

%S 25,35,49,55,77,115,121,161,235,253,295,329,413,415,517,529,535,581,

%T 649,749,835,895,913,1081,1135,1169,1177,1253,1315,1357,1589,1735,

%U 1795,1837,1841,1909,1915,1969,2209,2335,2395,2429,2461,2497,2513,2515,2681,2773,2815,2893,2935

%N Semiprimes m = p*q such that p-1 and q-1 are semiprimes.

%C Numbers of the form A005385(i)*A005385(j) for i,j >= 1. - _Altug Alkan_, Mar 22 2018

%H Robert Israel, <a href="/A193165/b193165.txt">Table of n, a(n) for n = 1..10000</a>

%e 1969 is in the sequence because 1969 = 11*179, and 11-1 = 2*5 and 179-1 = 2*89 are semiprimes.

%p with(numtheory):for n from 2 to 3000 do: x:=factorset(n):y:=bigomega(n):z:=x[1]:zz:=n/z:if y=2 and type(z,prime)=true and type(zz,prime) = true and bigomega(z-1)=2 and bigomega(zz-1)=2 then printf(`%d, `, n): else fi:od:

%p # Alternate:

%p N:= 10000: # to get all terms <= N

%p P:= select(p -> isprime(p) and numtheory:-bigomega(p-1)=2, [$1..N/5]):

%p nP:= nops(P):

%p sort(select(`<=`, [seq(seq(P[i]*P[j], i=1..j), j=1..nP)], N)); # _Robert Israel_, Mar 23 2018

%t spsQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},PrimeOmega[n] == PrimeOmega[First[f]-1] == PrimeOmega[Last[f]-1]==2]; Select[Range[ 3000], spsQ] (* _Harvey P. Dale_, Jul 27 2011 *)

%o (PARI) upTo(lim)=my(u=List(),v=List(),t);forprime(p=2,lim\5,if(isprime(p\2),listput(u,p)));for(i=1,#u,for(j=1,i,t=u[i]*u[j];if(t>lim,break,listput(v,t))));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 30 2011

%Y Subsequence of A001358.

%Y Cf. A005385, A193227.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jul 17 2011