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%I #10 Aug 25 2017 10:53:35
%S 35,55,77,115,161,235,253,295,329,413,415,517,535,581,649,749,835,895,
%T 913,1081,1135,1169,1177,1253,1315,1357,1589,1735,1795,1837,1841,1909,
%U 1915,1969,2335,2395,2429,2461,2497,2513,2515,2681,2773,2815,2893,2935
%N Products (semiprimes) of two distinct safe primes.
%C 35=5*7; 5 and 7 are safe primes, 55=5*11; 5 and 11 are safe primes,...
%H Michael De Vlieger, <a href="/A157352/b157352.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 35 since 35 = 5 * 7, and (5 - 1)/2 = 2 and (7 - 1)/2 = 3 are both prime, thus 5 and 7 are distinct safe primes.
%t lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=Length[First/@FactorInteger[n]];If[a==2,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];If[PrimeQ[(c-1)/2]&&PrimeQ[(d-1)/2],AppendTo[lst,n]]]],{n,7!}];lst
%t Select[Select[Range@ 3000, PrimeNu@ # == 2 &], Times @@ Map[If[PrimeQ[(# - 1)/2], #, 0] &, Map[First, FactorInteger@ #]] == # &] (* _Michael De Vlieger_, Feb 28 2016 *)
%t Module[{upto=3000,sp},sp=Select[Prime[Range[PrimePi[upto/5]]],PrimeQ[(#-1)/2]&];Select[Union[Times@@@Subsets[sp,{2}]],#<+upto&]] (* _Harvey P. Dale_, Aug 25 2017 *)
%Y Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009
%E Example corrected by _Harvey P. Dale_, Aug 25 2017