A349201 -id:A349201 - cp's OEIS frontend

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

Peter Luschny, Nov 10 2021

nonn

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

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

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

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

# 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

# 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);

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 *)

cp's OEIS Frontend

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

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