

A002376


Least number of positive cubes needed to represent n.
(Formerly M0466 N0170)


16



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

1,2


COMMENTS

No terms are greater than 9, see A002804.  Charles R Greathouse IV, Aug 01 2013


REFERENCES

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), 276280.


LINKS

T. D. Noe and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Eric Weisstein's World of Mathematics, Cubic Number


FORMULA

The g.f. conjectured by Simon Plouffe in his 1992 dissertation,
(1zz**2z**3z**4z**5z**6+6*z**7)/(z+1)/(z**2+1)/(z**4+1)/(z1)**2, is incorrect: the first wrong coefficient is that of z^26.  Robert Israel, Jun 30 2017


MAPLE

f:= proc(n) option remember;
min(seq(procname(n  i^3)+1, i=1..floor(n^(1/3))))
end proc:
f(0):= 0:
map(f, [$1..100]); # Robert Israel, Jun 30 2017


MATHEMATICA

CubesCnt[n_] := Module[{k = 1}, While[Length[PowersRepresentations[n, k, 3]] == 0, k++]; k]; Array[CubesCnt, 100] (* T. D. Noe, Apr 01 2011 *)


CROSSREFS

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).
Sequence in context: A338481 A338492 A338458 * A055401 A053829 A033928
Adjacent sequences: A002373 A002374 A002375 * A002377 A002378 A002379


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Arlin Anderson (starship1(AT)gmail.com)


STATUS

approved



