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A109470 Sum of first n noncubes. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... + n)^2. Note that the sum of noncubes can be a cube: a(6) = 3^3. Note that the sum of noncubes can be a square: a(4) = 3^2, a(7) = 6^2, a(15) = 12^2, a(37) = 28^2, a(69) = 51^2. Primes in this sequence include a(1) = 2, a(2) = 5, a(14) = 127, a(17) = 181, a(62) = 2111, a(73) = 2903, a(77) = 3221.
LINKS
FORMULA
a(n) = Sum_{i=1..n} A007412(i).
a(n) = Sum_{i=1..n} (i + floor((i + floor(i^(1/3))^(1/3))).
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
EXAMPLE
a(6) = 2 + 3 + 4 + 5 + 6 + 7 = 27.
a(7) = 2 + 3 + 4 + 5 + 6 + 7 + 9 = 36.
MATHEMATICA
Accumulate[With[{no=60}, Complement[Range[no], Range[Floor[Power[no, (3)^-1]]]^3]]] (* Harvey P. Dale, Feb 14 2011 *)
CROSSREFS
Sequence in context: A132337 A000096 A134189 * A112873 A048093 A024669
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 28 2005
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)