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

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, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,1

Comments

Numbers that are not the sum of the first k cubes.

Links

Paolo Xausa, Table of n, a(n) for n = 1..11011

Eric Weisstein's World of Mathematics, Triangular Number

Formula

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)).

Mathematica

A376573[n_] := With[{m = Floor[(4*n)^(1/4)]}, n + m - Boole[4*n <= m*(m - 1)*(m*(m + 3) + 4)]];
Array[A376573, 96] (* or *)
Complement[Range[Last[#]], #] & [Accumulate[Range[4]^3]] (* Paolo Xausa, Oct 04 2024 *)

Prog

(Python)
from sympy import integer_nthroot
def A376573(n): return n+(m:=integer_nthroot(k:=n<<2, 4)[0])-(k<=m*(m-1)*(m**2+3*m+4))
(PARI) isok(k) = !issquare(k) || (issquare(k) && !ispolygonal(sqrtint(k), 3)); \\ Michel Marcus, Oct 02 2024

Crossrefs

Cf. A000537, A302058.

Sequence in context: A265556 A358123 A004728 * A072886 A031980 A183221

Adjacent sequences: A376570 A376571 A376572 * A376574 A376575 A376576

Keyword

nonn,easy

Author

Chai Wah Wu, Oct 02 2024

Status

approved