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

Author

N. J. A. Sloane, Apr 22 2013

Keywords

• nonn

Examples

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

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

Crossrefs

Cf. A001694, A036966.

Programs

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 *)

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

Extensions

More terms from Amiram Eldar, Jan 30 2023