A344780 Semiprimes that are product of two distinct Honaker primes.

34453, 59867, 120191, 136109, 137419, 142921, 170431, 178291, 187723, 205801, 250603, 253223, 273257, 275887, 280471, 286933, 290951, 297763, 319771, 339421, 342163, 348853, 354617, 356189, 357499, 357943, 367193, 376879, 401777, 410947, 413173, 422999, 449723

Offset: 1

Author

K. D. Bajpai, May 28 2021

Keywords

• nonn
• base

Comments

Subsequence of A006881.

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

Examples

			34453 = 131*263 which are distinct Honaker primes.
120191 = 263*457 which are distinct Honaker primes.
		

Crossrefs

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

Programs

Maple

isA006881 := proc(n)
    if numtheory[bigomega](n) =2 and A001221(n) = 2 then
        true ;
    else
        false ;
    end if;
end proc:
isA344780 := proc(n)
    if isA006881(n) then
        for p in ifactors(n)[2] do
            if not isA033548(op(1,p)) then
                return false;
            end if;
        end do:
        true ;
    else
        false;
    end if;
end proc:
for n from 1  do
    if isA344780(n) then
        printf("%d,\n",n);
    end if;
end do: # R. J. Mathar, Jul 07 2021

Mathematica

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