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A344780 Semiprimes that are product of two distinct Honaker primes.

%I A344780 #28 Jul 07 2021 06:09:41
%S A344780 34453,59867,120191,136109,137419,142921,170431,178291,187723,205801,
%T A344780 250603,253223,273257,275887,280471,286933,290951,297763,319771,
%U A344780 339421,342163,348853,354617,356189,357499,357943,367193,376879,401777,410947,413173,422999,449723
%N A344780 Semiprimes that are product of two distinct Honaker primes.
%C A344780 Subsequence of A006881.
%C A344780 a(1) = 34453 is the only number <= 5*10^6 that is a triangular number.
%e A344780 34453 = 131*263 which are distinct Honaker primes.
%e A344780 120191 = 263*457 which are distinct Honaker primes.
%p A344780 isA006881 := proc(n)
%p A344780     if numtheory[bigomega](n) =2 and A001221(n) = 2 then
%p A344780         true ;
%p A344780     else
%p A344780         false ;
%p A344780     end if;
%p A344780 end proc:
%p A344780 isA344780 := proc(n)
%p A344780     if isA006881(n) then
%p A344780         for p in ifactors(n)[2] do
%p A344780             if not isA033548(op(1,p)) then
%p A344780                 return false;
%p A344780             end if;
%p A344780         end do:
%p A344780         true ;
%p A344780     else
%p A344780         false;
%p A344780     end if;
%p A344780 end proc:
%p A344780 for n from 1  do
%p A344780     if isA344780(n) then
%p A344780         printf("%d,\n",n);
%p A344780     end if;
%p A344780 end do: # _R. J. Mathar_, Jul 07 2021
%t A344780 fHQ[n_] := Plus @@ IntegerDigits@n == Plus @@ IntegerDigits@PrimePi@n;
%t A344780 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[fHQ[c] && fHQ[d], AppendTo[lst, {n,c,d}]]]], {n, 2000000}]; lst
%Y A344780 Cf. A006881, A033548, A144482, A144856, A333788.
%K A344780 nonn,base
%O A344780 1,1
%A A344780 _K. D. Bajpai_, May 28 2021