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A344780 Semiprimes that are product of two distinct Honaker primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 11:44 EST 2021. Contains 349440 sequences. (Running on oeis4.)