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A180499
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n^3 + n-th cubefree number.
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1
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2, 10, 30, 68, 130, 222, 350, 521, 739, 1011, 1343, 1741, 2211, 2759, 3392, 4114, 4932, 5852, 6880, 8022, 9284, 10673, 12193, 13852, 15654, 17606, 19714, 21985, 24423, 27035, 29827, 32805, 35975, 39343
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OFFSET
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1,1
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COMMENTS
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First differs from n^3 + n (A034262) at n=8 because 8 is the first positive integer which is not cubefree. What cubes appear in this sequence? The subsequence of primes (for n = 1, 8, 9, 12, 34, 69, 104, 105, 109, 131, 134, 151, 154, 172, 173, 184, 197, 198, 201, 213, ...) begins: 2, 521, 739, 1741, 39343, 328591, 1124987, 1157749, 1295159, 2248247, 2406263, 3443131, 3652447, 5088653, 5177923, 6229723, 7645607, 7762627, 8120839, 9663851.
No cubes appear in this sequence: the n-th cubefree number is asymptotically zeta(3)*n, putting members of this sequence strictly between n^3 and (n+1)^3. (Lacking effective error bounds this actually only shows that there are finitely many.) - Charles R Greathouse IV, Jan 21 2011
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = n^3 + A004709(n) = A000578(n) + A004709(n).
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EXAMPLE
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a(8) = 8^3 + 8th number that is not divisible by any cube > 1 = 8^3 + 9 = 521.
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MATHEMATICA
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#[[1]]+#[[2]]^3&/@Module[{cf=Select[Range[50], Max[FactorInteger[#][[All, 2]]] < 3&]}, Thread[{cf, Range[Length[cf]]}]] (* Harvey P. Dale, Jun 28 2020 *)
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CROSSREFS
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Cf. A000578, A034262, A161203.
Sequence in context: A162524 A065137 A034262 * A167214 A034827 A328532
Adjacent sequences: A180496 A180497 A180498 * A180500 A180501 A180502
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KEYWORD
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nonn,easy
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AUTHOR
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Jonathan Vos Post, Jan 20 2011
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STATUS
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approved
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