A210470 Powerful numbers (A001694) which can be written as the sum of two relatively prime 3-powerful numbers (A036966) different from 1.

841, 968, 2312, 3528, 5041, 5776, 12769, 14884, 16641, 45125, 51984, 109561, 123823, 157609, 168921, 207576, 373321, 450241, 498436, 609725, 711828, 731025, 798768, 940896, 1223048, 1590121, 1792921, 2478843, 2481992, 2526752, 3157729, 3964081, 5346675, 6255001

Offset

1,1

References

Jean-Marie de Konninck, Those Fascinating Numbers, Amer. Math. Soc., 2009.

Alonso Del Arte, Posting to the Sequence Fans Mailing List, Mar 10 2011.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Formula

{ a in A001694: a=b+c and b,c >1 and b,c in A036966 and gcd(b,c)=1}. - R. J. Mathar, May 01 2013

Example

841 = 216+625 ; 968 = 343+625 ; 2312=125+2187;

Maple

isA210470 := proc(n)
    if isA001694(n) then
        for i from 2 do
            p3 := A036966(i) ;
            if p3+2 > n then
                return false;
            end if;
            p3comp := n-p3 ;
            if isA036966(p3comp) and igcd(p3, p3comp) = 1 then
                # print(n, p3, p3comp) ;
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 1 do
    if isA210470(n) then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, May 01 2013

Mathematica

With[{max = 10^7}, powQ[n_, e_] := Min[FactorInteger[n][[;; , 2]]] > e; pows = Union[Flatten[Table[i^2*j^3, {j, max^(1/3)}, {i, Sqrt[max/j^3]}]]]; Select[Union[Plus @@@ Select[Tuples[Select[pows, powQ[#, 2] &], {2}], CoprimeQ @@ # &]], # < max && powQ[#, 1] &]] (* Amiram Eldar, Jan 30 2023 *)

Crossrefs

Cf. A001694, A036966.

Sequence in context: A364264 A362440 A159690 * A108324 A133496 A361675

Adjacent sequences: A210467 A210468 A210469 * A210471 A210472 A210473

Keyword

nonn

Author

N. J. A. Sloane, Apr 22 2013

Extensions

More terms from Amiram Eldar, Jan 30 2023

Status

approved