A344780 - OEIS

%I #28 Jul 07 2021 06:09:41

%S 34453,59867,120191,136109,137419,142921,170431,178291,187723,205801,

%T 250603,253223,273257,275887,280471,286933,290951,297763,319771,

%U 339421,342163,348853,354617,356189,357499,357943,367193,376879,401777,410947,413173,422999,449723

%N Semiprimes that are product of two distinct Honaker primes.

%C Subsequence of A006881.

%C a(1) = 34453 is the only number <= 5*10^6 that is a triangular number.

%e 34453 = 131*263 which are distinct Honaker primes.

%e 120191 = 263*457 which are distinct Honaker primes.

%p isA006881 := proc(n)

%p     if numtheory[bigomega](n) =2 and A001221(n) = 2 then

%p         true ;

%p     else

%p         false ;

%p     end if;

%p end proc:

%p isA344780 := proc(n)

%p     if isA006881(n) then

%p         for p in ifactors(n)[2] do

%p             if not isA033548(op(1,p)) then

%p                 return false;

%p             end if;

%p         end do:

%p         true ;

%p     else

%p         false;

%p     end if;

%p end proc:

%p for n from 1  do

%p     if isA344780(n) then

%p         printf("%d,\n",n);

%p     end if;

%p end do: # _R. J. Mathar_, Jul 07 2021

%t fHQ[n_] := Plus @@ IntegerDigits@n == Plus @@ IntegerDigits@PrimePi@n;

%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[fHQ[c] && fHQ[d], AppendTo[lst, {n,c,d}]]]], {n, 2000000}]; lst

%Y Cf. A006881, A033548, A144482, A144856, A333788.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, May 28 2021