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

1,1

Comments

Subsequence of A006881.

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

Links

Table of n, a(n) for n=1..33.

Example

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

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

Crossrefs

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

Sequence in context: A233872 A055001 A164556 * A068703 A225025 A081428

Adjacent sequences: A344777 A344778 A344779 * A344781 A344782 A344783

Keyword

nonn,base

Author

K. D. Bajpai, May 28 2021

Status

approved