A132296 Sum of the noncube numbers less than or equal to n.

0, 2, 5, 9, 14, 20, 27, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449

Offset: 1

Author

Cino Hilliard, Nov 07 2007

Keywords

• nonn

Examples

			Let n=10. The sum of the noncube numbers <= 10 is 2+3+4+5+6+7+9+10 = 46, the 10th entry in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Accumulate[Table[If[IntegerQ[n^(1/3)],0,n],{n,60}]] (* Harvey P. Dale, Oct 16 2012 *)

PARI

g(n)=for(x=1,n,r=floor(x^(1/3));sumcu=(r*(r+1)/2)^2;sn=x*(x+1)/2;print1(sn-sumcu","))

Python

from sympy import integer_nthroot
def A132296(n): return n*(n+1)-(((r:=integer_nthroot(n,3)[0])*(r+1))**2>>1)>>1 # Chai Wah Wu, Sep 03 2024

Formula

Let r = floor(n^(1/3)) = A048766(n). Then a(n) = n(n+1)/2 - (r(r+1)/2)^2 = A000217(n)-A000537(r).