cp's OEIS Frontend

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

%I A348897 #35 Oct 23 2023 04:47:33
%S A348897 0,1,4,8,15,27,32,40,64,65,85,108,120,125,156,175,203,216,256,259,272,
%T A348897 320,343,369,400,405,477,500,512,520,580,585,671,680,715,729,803,820,
%U A348897 864,888,935,960,1000,1080,1105,1111,1157,1248,1261,1331,1372,1400,1417
%N A348897 Numbers of the form (x + y)*(x^2 + y^2).
%C A348897 Also numbers of the form (x - i*y)*(x + i*y)*(x + y).
%C A348897 Loeschian numbers of this form are A349200.
%C A348897 A349201 and A349202 are subsequences of this sequence.
%C A348897 Numbers of the form 1 + n + n^2 + n^3 (A053698) are a subsequence.
%C A348897 Numbers of the form n^3 + n^4 + n^5 + n^6 are a subsequence.
%C A348897 Numbers of the form 1 + n^2 + n^4 + n^6 (A059830) are a subsequence. - _Bernard Schott_, Nov 11 2021
%H A348897 Peter Luschny, <a href="/A348897/b348897.txt">Table of n, a(n) for n = 1..1200</a>
%e A348897 1010101 is in this sequence because 1010101 = (100 + 1)*(100^2 + 1^2).
%p A348897 # Returns the terms less than or equal to b^3.
%p A348897 A348897List := proc(b) local n, k, a, b3, R;
%p A348897 b3 := abs(b^3); R := {};
%p A348897 for n from 0 to b do for k from 0 to n do
%p A348897     a := (n + k)*(n^2 + k^2);
%p A348897     if a > b3 then break fi;
%p A348897     R := R union {a};
%p A348897 od od; sort(R) end:
%p A348897 A348897List(12);
%t A348897 max = 2000;
%t A348897 xmax = max^(1/3) // Ceiling;
%t A348897 Table[(x + y) (x^2 + y^2), {x, 0, xmax}, {y, x, xmax}] // Flatten // Union // Select[#, # <= max&]& (* _Jean-François Alcover_, Oct 23 2023 *)
%o A348897 (Julia) # Returns the terms less than or equal to b^3.
%o A348897 function A348897List(b)
%o A348897     b3 = b^3; R = [0]
%o A348897     for n in 1:b
%o A348897         for k in 0:n
%o A348897             a = (n + k) * (n^2 + k^2)
%o A348897             a > b3 && break
%o A348897             push!(R, a)
%o A348897     end end
%o A348897 unique!(sort!(R)) end
%o A348897 A348897List(12) |> println
%Y A348897 Cf. A198063, A321500, A003136, A053698, A059830, A349200, A349201, A349202.
%K A348897 nonn
%O A348897 1,3
%A A348897 _Peter Luschny_, Nov 10 2021