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A114286
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Sum of the cubes of the first n cubefree numbers.
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1
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0, 1, 9, 36, 100, 225, 441, 784, 1513, 2513, 3844, 5572, 7769, 10513, 13888, 18801, 24633, 31492, 39492, 48753, 59401, 71568, 87193, 104769, 126721, 151110, 178110, 207901, 243838, 283142, 326017, 372673, 423326, 478198, 537517, 606438, 680526
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A114287 is the sum of the cubes of the cubeful numbers A046099. a(n) is prime for a(13) = 10513, a(45) = 1653409. a(n) is semiprime for n = 2, 8, 9, 12, 20, 30, 31, 32, 34, 37, 40, 47. a(n) is a perfect square for n = 0, 1, 2, 3, 4, 5, 6, 7, 10.
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LINKS
| Eric Weisstein's World of Mathematics, Cubefree.
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FORMULA
| a(n) = 1^3 + ... + A004709(n)^3. (Sum of the cubes of the cubeful numbers A046099 =< n) + (Sum of the cubes of the cube-free numbers A004709 =< n) = (Sum of the cubes of the numbers =< n) = A000537 = Sum of first n cubes; or n-th triangular number squared = (A000217(n))^2.
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EXAMPLE
| 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 9^3 + 10^3 + 11^3 = 3844 = 2^2 * 31^2.
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CROSSREFS
| Cf. A000217, A000537, A004709, A005117, A013929, A046099, A111715, A111732, A114287.
Sequence in context: A085037 A169835 A000537 * A098928 A139469 A103158
Adjacent sequences: A114283 A114284 A114285 * A114287 A114288 A114289
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 20 2005
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