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A132296
Sum of the noncube numbers less than or equal to n.
2
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
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Nov 07 2007
STATUS
approved