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A022551 Numbers that are the sum of 2 squares and a nonnegative cube.

%I A022551 #21 Jul 08 2025 09:17:06
%S A022551 0,1,2,3,4,5,6,8,9,10,11,12,13,14,16,17,18,19,20,21,24,25,26,27,28,29,
%T A022551 30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U A022551 54,56,57,58,59,60,61,62
%N A022551 Numbers that are the sum of 2 squares and a nonnegative cube.
%H A022551 Jean-François Alcover, <a href="/A022551/b022551.txt">Table of n, a(n) for n = 1..943</a>
%H A022551 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%p A022551 isA022551 := proc(n)
%p A022551     local a,b,c ;
%p A022551     for c from 0 do
%p A022551         if c^3 > n then
%p A022551             return false;
%p A022551         end if;
%p A022551         for a from 0 do
%p A022551             b2 := n-c^3-a^2 ;
%p A022551             if b2 < a^2 then
%p A022551                 break;
%p A022551             end if;
%p A022551             if issqr(b2) then
%p A022551                 return true;
%p A022551             end if;
%p A022551         end do:
%p A022551     end do:
%p A022551 end proc: # _R. J. Mathar_, Sep 02 2016
%t A022551 max = 1000;
%t A022551 Table[x^2 + y^2 + z^3, {x, 0, Sqrt[max]}, {y, x, Sqrt[max - x^2]}, {z, 0, (max - x^2 - y^2)^(1/3)}] // Flatten // Union // Select[#, # <= max&]& (* _Jean-François Alcover_, Mar 23 2020 *)
%Y A022551 Complement of A022552.
%K A022551 nonn
%O A022551 1,3
%A A022551 _N. J. A. Sloane_