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A002376
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Least number of positive cubes needed to sum to n.
(Formerly M0466 N0170)
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16
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1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 1, 2, 3, 4, 5, 4, 5, 6, 2, 3, 4, 5, 6, 5, 6, 7, 3, 4, 5, 6, 7, 6, 7, 8, 4, 5, 6, 2, 3, 4, 5, 6, 5, 6, 7, 3, 4, 1, 2, 3, 4, 5, 6, 4, 5, 2, 3, 4, 5, 6, 7, 5, 6, 3, 3, 4, 5, 6, 7, 6, 7, 4, 4, 5, 2, 3, 4, 5, 6, 5, 5, 6, 3, 4, 5, 6, 7, 6, 6
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 81.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. R. Zornow, De compositione numerorum e cubis integris positivus, J. Reine Angew. Math., 14 (1835), 276-280.
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LINKS
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FORMULA
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The g.f. conjectured by Simon Plouffe in his 1992 dissertation,
-(-1-z-z^2-z^3-z^4-z^5-z^6+6*z^7)/(z+1)/(z^2+1)/(z^4+1)/(z-1)^2, is incorrect: the first wrong coefficient is that of z^26. - Robert Israel, Jun 30 2017
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MAPLE
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f:= proc(n) option remember;
min(seq(procname(n - i^3)+1, i=1..floor(n^(1/3))))
end proc:
f(0):= 0:
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MATHEMATICA
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CubesCnt[n_] := Module[{k = 1}, While[Length[PowersRepresentations[n, k, 3]] == 0, k++]; k]; Array[CubesCnt, 100] (* T. D. Noe, Apr 01 2011 *)
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CROSSREFS
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Cf. A000578, A003325 (numbers requiring 2 cubes), A047702 (numbers requiring 3 cubes), A047703 (numbers requiring 4 cubes), A047704 (numbers requiring 5 cubes), A046040 (numbers requiring 6 cubes), A018890 (numbers requiring 7 cubes), A018888 (numbers requiring 8 or 9 cubes), A055401 (cubes needed by greedy algorithm).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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More terms from Arlin Anderson (starship1(AT)gmail.com)
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STATUS
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approved
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