A348897 Numbers of the form (x + y)*(x^2 + y^2).

0, 1, 4, 8, 15, 27, 32, 40, 64, 65, 85, 108, 120, 125, 156, 175, 203, 216, 256, 259, 272, 320, 343, 369, 400, 405, 477, 500, 512, 520, 580, 585, 671, 680, 715, 729, 803, 820, 864, 888, 935, 960, 1000, 1080, 1105, 1111, 1157, 1248, 1261, 1331, 1372, 1400, 1417

Offset: 1

Author

Peter Luschny, Nov 10 2021

Keywords

• nonn

Comments

Also numbers of the form (x - i*y)*(x + i*y)*(x + y).

Loeschian numbers of this form are A349200.

A349201 and A349202 are subsequences of this sequence.

Numbers of the form 1 + n + n^2 + n^3 (A053698) are a subsequence.

Numbers of the form n^3 + n^4 + n^5 + n^6 are a subsequence.

Numbers of the form 1 + n^2 + n^4 + n^6 (A059830) are a subsequence. - Bernard Schott, Nov 11 2021

Examples

			1010101 is in this sequence because 1010101 = (100 + 1)*(100^2 + 1^2).
		

Links

• Peter Luschny, Table of n, a(n) for n = 1..1200

Crossrefs

Cf. A198063, A321500, A003136, A053698, A059830, A349200, A349201, A349202.

Programs

Julia

# Returns the terms less than or equal to b^3.
function A348897List(b)
    b3 = b^3; R = [0]
    for n in 1:b
        for k in 0:n
            a = (n + k) * (n^2 + k^2)
            a > b3 && break
            push!(R, a)
    end end
unique!(sort!(R)) end
A348897List(12) |> println

Maple

# Returns the terms less than or equal to b^3.
A348897List := proc(b) local n, k, a, b3, R;
b3 := abs(b^3); R := {};
for n from 0 to b do for k from 0 to n do
    a := (n + k)*(n^2 + k^2);
    if a > b3 then break fi;
    R := R union {a};
od od; sort(R) end:
A348897List(12);

Mathematica

max = 2000;
xmax = max^(1/3) // Ceiling;
Table[(x + y) (x^2 + y^2), {x, 0, xmax}, {y, x, xmax}] // Flatten // Union // Select[#, # <= max&]& (* Jean-François Alcover, Oct 23 2023 *)