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A152015
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a(n) = n^3 - n^2 - n.
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5
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0, -1, 2, 15, 44, 95, 174, 287, 440, 639, 890, 1199, 1572, 2015, 2534, 3135, 3824, 4607, 5490, 6479, 7580, 8799, 10142, 11615, 13224, 14975, 16874, 18927, 21140, 23519, 26070, 28799, 31712, 34815, 38114, 41615, 45324, 49247, 53390, 57759, 62360
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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For n > 1, these are also the largest positive integers k such that k + n divides k^3 + n^2. For all n > 1 and p > 1, the largest positive integer k such that k + n divides k^p + n^(p-1) is given by k = n^p - (-n)^(p-1) - n. Here, p = 3. - Derek Orr, Aug 13 2014
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LINKS
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FORMULA
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MAPLE
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a:=n->sum(-1+sum(1+sum(1, i=2..n), j=2..n), k=1..n): seq(a(n), n=0..44); # Zerinvary Lajos, Dec 22 2008
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MATHEMATICA
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lst={}; Do[AppendTo[lst, n^3-n^2-n], {n, 0, 5!}]; lst
LinearRecurrence[{4, -6, 4, -1}, {0, -1, 2, 15}, 50] (* Harvey P. Dale, Sep 08 2024 *)
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PROG
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(PARI) vector(100, n, (n-1)^3-(n-1)^2-(n-1)) \\ Derek Orr, Aug 13 2014
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CROSSREFS
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KEYWORD
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sign,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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