

A188462


Least number of 5th powers needed to represent n.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
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OFFSET

1,2


COMMENTS

Vaughan & Wooley (1995) prove that a(n) <= 17 for large enough n; in fact it is conjectured that a(n) <= 6 for large enough n. The maximum value is a(223) = 37.  Charles R Greathouse IV, Jul 05 2017


LINKS

R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, Number theory for the millennium, III (Urbana, IL, 2000), 301340, A K Peters, Natick, MA, 2002.


EXAMPLE

33 = 2^5 + 1^5 (least decomposition) hence a(33) = 2.


MATHEMATICA

Cnt5[n_] := Module[{k = 1}, While[Length[PowersRepresentations[n, k, 5]] == 0, k++]; k]; Array[Cnt5, 105] (* T. D. Noe, Apr 01 2011 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



