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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 cube: a(6) = 3^3. Note that the sum of noncubes can be 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

Table of n, a(n) for n=1..53.

FORMULA

a(n) = SUM{from i = 1 to n} A007412(i). a(n) = SUM{from i = 1 to n} (i +[(i+[i^{1/3}])^{1/3}]) where [x] = floor(x). a(n) = A000217(A007412(n)) - SUM{from i = 1 to [(A007412(n)^(1/3))]} i^3. a(n) = A000217(A007412(n)) - (A000217([(A007412(n))^(1/3)])^2).

Set R=a007412(n), S=FLOOR(R^(1/3)), then a(n)=(R*(R+1))/2-((S*(S+1))/2)^2 [From 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

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

Sequence in context: A132337 A000096 A134189 * A112873 A048093 A024669

Adjacent sequences:  A109467 A109468 A109469 * A109471 A109472 A109473

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 28 2005

STATUS

approved

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Last modified March 28 02:14 EDT 2017. Contains 284182 sequences.