A348897 - OEIS

%I #35 Oct 23 2023 04:47:33

%S 0,1,4,8,15,27,32,40,64,65,85,108,120,125,156,175,203,216,256,259,272,

%T 320,343,369,400,405,477,500,512,520,580,585,671,680,715,729,803,820,

%U 864,888,935,960,1000,1080,1105,1111,1157,1248,1261,1331,1372,1400,1417

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

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

%C Loeschian numbers of this form are A349200.

%C A349201 and A349202 are subsequences of this sequence.

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

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

%C Numbers of the form 1 + n^2 + n^4 + n^6 (A059830) are a subsequence. - _Bernard Schott_, Nov 11 2021

%H Peter Luschny, <a href="/A348897/b348897.txt">Table of n, a(n) for n = 1..1200</a>

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

%p # Returns the terms less than or equal to b^3.

%p A348897List := proc(b) local n, k, a, b3, R;

%p b3 := abs(b^3); R := {};

%p for n from 0 to b do for k from 0 to n do

%p     a := (n + k)*(n^2 + k^2);

%p     if a > b3 then break fi;

%p     R := R union {a};

%p od od; sort(R) end:

%p A348897List(12);

%t max = 2000;

%t xmax = max^(1/3) // Ceiling;

%t Table[(x + y) (x^2 + y^2), {x, 0, xmax}, {y, x, xmax}] // Flatten // Union // Select[#, # <= max&]& (* _Jean-François Alcover_, Oct 23 2023 *)

%o (Julia) # Returns the terms less than or equal to b^3.

%o function A348897List(b)

%o     b3 = b^3; R = [0]

%o     for n in 1:b

%o         for k in 0:n

%o             a = (n + k) * (n^2 + k^2)

%o             a > b3 && break

%o             push!(R, a)

%o     end end

%o unique!(sort!(R)) end

%o A348897List(12) |> println

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

%K nonn

%O 1,3

%A _Peter Luschny_, Nov 10 2021