A302058 Numbers that are not square pyramidal numbers.

2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset: 1

Author

Ilya Gutkovskiy, Mar 31 2018

Keywords

• nonn
• easy

Comments

Numbers not of the form 0^2 + 1^2 + 2^2 + ... + m^2 = m*(m + 1)*(2*m + 1)/6.

Links

• Eric Weisstein's World of Mathematics, Square Pyramidal Number

Crossrefs

Complement of A000330.

Cf. A000037, A014132, A145397, A253903.

Programs

Mathematica

Module[{nn=6,m},m=(nn(nn+1)(2nn+1))/6 ;Complement[Range[m],Table[(n(n+1)(2n+1))/6,{n,nn}]]] (* Harvey P. Dale, Aug 22 2020 *)

Python

from sympy import integer_nthroot
def A302058(n): return n+(m:=integer_nthroot(3*n,3)[0])-(6*n<=m*(m-1)*(2*m+5)) # Chai Wah Wu, Oct 01 2024

Formula

a(n) = n+m if 6n>m(m-1)(2m+5) and a(n) = n+m-1 otherwise where m = floor((3n)^(1/3)). - Chai Wah Wu, Oct 01 2024