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A109470 Sum of first n noncubes. 0

%I

%S 2,5,9,14,20,27,36,46,57,69,82,96,111,127,144,162,181,201,222,244,267,

%T 291,316,342,370,399,429,460,492,525,559,594,630,667,705,744,784,825,

%U 867,910,954,999,1045,1092,1140,1189,1239,1290,1342,1395,1449,1504,1560

%N Sum of first n noncubes.

%C 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.

%F a(n) = Sum_{i=1..n} A007412(i).

%F a(n) = Sum_{i=1..n} (i + floor((i + floor(i^(1/3))^(1/3))).

%F a(n) = A000217(A007412(n)) - Sum_{i=1..floor((A007412(n)^(1/3)))} i^3.

%F a(n) = A000217(A007412(n)) - A000217(floor(A007412(n)^(1/3)))^2.

%F 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

%e a(6) = 2 + 3 + 4 + 5 + 6 + 7 = 27.

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

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

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

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 28 2005

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Last modified April 20 18:45 EDT 2021. Contains 343137 sequences. (Running on oeis4.)