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A109470
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Sum of first n noncubes.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} (i + floor((i + floor(i^(1/3))^(1/3))).
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
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EXAMPLE
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a(6) = 2 + 3 + 4 + 5 + 6 + 7 = 27.
a(7) = 2 + 3 + 4 + 5 + 6 + 7 + 9 = 36.
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MATHEMATICA
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Accumulate[With[{no=60}, Complement[Range[no], Range[Floor[Power[no, (3)^-1]]]^3]]] (* Harvey P. Dale, Feb 14 2011 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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