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A376573 Numbers that are not squares of triangular numbers. Complement of A000537.

%I A376573 #27 Oct 04 2024 10:04:16
%S A376573 2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%T A376573 28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A376573 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A376573 Numbers that are not squares of triangular numbers. Complement of A000537.
%C A376573 Numbers that are not the sum of the first k cubes.
%H A376573 Paolo Xausa, <a href="/A376573/b376573.txt">Table of n, a(n) for n = 1..11011</a>
%H A376573 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>
%F A376573 a(n) = n+m if 4n>m*(m-1)*(m^2+3*m+4) and a(n) = n+m-1 otherwise where m = floor((4n)^(1/4)).
%t A376573 A376573[n_] := With[{m = Floor[(4*n)^(1/4)]}, n + m - Boole[4*n <= m*(m - 1)*(m*(m + 3) + 4)]];
%t A376573 Array[A376573, 96] (* or *)
%t A376573 Complement[Range[Last[#]], #] & [Accumulate[Range[4]^3]] (* _Paolo Xausa_, Oct 04 2024 *)
%o A376573 (Python)
%o A376573 from sympy import integer_nthroot
%o A376573 def A376573(n): return n+(m:=integer_nthroot(k:=n<<2,4)[0])-(k<=m*(m-1)*(m**2+3*m+4))
%o A376573 (PARI) isok(k) = !issquare(k) || (issquare(k) && !ispolygonal(sqrtint(k), 3)); \\ _Michel Marcus_, Oct 02 2024
%Y A376573 Cf. A000537, A302058.
%K A376573 nonn,easy
%O A376573 1,1
%A A376573 _Chai Wah Wu_, Oct 02 2024