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A302058
Numbers that are not square pyramidal numbers.
4
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
1,1
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
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
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 *)
PROG
(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
CROSSREFS
Complement of A000330.
Sequence in context: A230313 A052413 A276389 * A183302 A323733 A003247
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Mar 31 2018
STATUS
approved