A064524 -id:A064524 - cp's OEIS frontend

A109470 Sum of first n noncubes.

2, 5, 9, 14, 20, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 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, 1504, 1560

Offset: 1

Jonathan Vos Post, Aug 28 2005

			a(6) = 2 + 3 + 4 + 5 + 6 + 7 = 27.
a(7) = 2 + 3 + 4 + 5 + 6 + 7 + 9 = 36.

Cf. A000537, A007412, A048766, A064524, A086849.

Accumulate[With[{no=60},Complement[Range[no],Range[Floor[Power[no, (3)^-1]]]^3]]]  (* Harvey P. Dale, Feb 14 2011 *)

a(n) = sum(i=1, n, i + sqrtnint(i + sqrtnint(i, 3), 3)); \\ Michel Marcus, Jun 20 2024

from sympy import integer_nthroot
def A109470(n): return ((m:=n+(k:=integer_nthroot(n,3)[0])+int(n>=(k+1)**3-k))*(m+1)>>1)-((r:=integer_nthroot(m,3)[0])*(r+1)>>1)**2 # Chai Wah Wu, Jun 17 2024

a(n) = Sum_{i=1..n} A007412(i).
a(n) = A000217(A007412(n)) - Sum_{i=1..floor((A007412(n)^(1/3)))} i^3.
a(n) = A000217(A007412(n)) - A000217(floor(A007412(n)^(1/3)))^2.
Let R = A007412(n) and S = floor(R^(1/3)); then a(n) = (R*(R+1))/2 - ((S*(S+1))/2)^2. - Gerald Hillier, Dec 21 2008

A139179 Number of non-fourth-powers <= n.

Original entry on oeis.org

0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 0

Jonathan Vos Post, Jun 06 2008

Cf. A028391, A064524.

a[n_] := n - Floor[n^(1/4)]; a /@ Range[0, 72] (* Giovanni Resta, Jun 21 2016 *)

from sympy import integer_nthroot
def A139179(n): return n-integer_nthroot(n,4)[0] # Chai Wah Wu, Jun 18 2024

a(n) = n - floor(n^(1/4)).

Offset corrected by Giovanni Resta, Jun 21 2016

cp's OEIS Frontend

A109470 Sum of first n noncubes.

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