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A348897
Numbers of the form (x + y)*(x^2 + y^2).
4
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
1,3
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
LINKS
EXAMPLE
1010101 is in this sequence because 1010101 = (100 + 1)*(100^2 + 1^2).
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 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 10 2021
STATUS
approved