A123053 Sum of a positive square, a positive cube and a positive fourth power.

3, 6, 10, 11, 13, 18, 21, 25, 26, 27, 28, 29, 32, 33, 34, 37, 38, 40, 42, 44, 45, 47, 49, 51, 52, 53, 58, 59, 60, 64, 66, 68, 69, 73, 74, 77, 79, 81, 83, 84, 86, 88, 89, 90, 91, 92, 93, 96, 98, 101, 102, 105, 107, 109, 112, 114, 116, 117, 118, 123, 124, 125

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

{A000290 \ 0} + {A000578 \ 0} + {A000583}. {a^4 + b^3 + c^2 for a,b,c>0}.

Example

a(1) = 3 = 1^4 + 1^3 + 1^2.
a(2) = 6 = 1^4 + 1^3 + 2^2.
a(3) = 10 = 1^4 + 2^3 + 1^2.
a(4) = 11 = 1^4 + 1^3 + 3^2.
a(5) = 13 = 1^4 + 2^3 + 2^2.
a(6) = 18 = 1^4 + 1^3 + 4^2 = 1^4 + 2^3 + 3^2 = 2^4 + 1^3 + 1^2.

Maple

isA123053 := proc(n)
    local x, y, z ;
    for x from 1 do
        if x^2 > n then
            return false;
        end if;
        for y from 1 do
            if x^2+y^3> n then
                break;
            end if;
            for z from 1 do
                if x^2+y^3+z^4 > n then
                    break;
                elif x^2+y^3+z^4 = n then
                    return true;
                end if;
            end do:
        end do:
    end do:
end proc:
n := 1 ;
for c from 0 to 10000 do
    if isA123053(c) then
        printf("%d %d\n", n, c) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Sep 07 2020

Mathematica

Select[ Union[ Total /@ Tuples[{Range[64]^2, Range[8]^4, Range[16]^3}]], # < 200 &] (* Giovanni Resta, Jun 12 2016 *)

Crossrefs

Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A055394 (numbers that are the sum of a positive square and a positive cube).

Sequence in context: A043321 A241858 A231668 * A221129 A138289 A219638

Adjacent sequences: A123050 A123051 A123052 * A123054 A123055 A123056

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 25 2006

Extensions

38, 86, and 93 added and 108 deleted by Giovanni Resta, Jun 12 2016

Status

approved