A132296 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

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).

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

CROSSREFS

Sequence in context: A130029 A266450 A361742 * A275586 A333449 A075543

Adjacent sequences: A132293 A132294 A132295 * A132297 A132298 A132299

KEYWORD

nonn

AUTHOR

Cino Hilliard, Nov 07 2007

STATUS

approved