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A174406 a(n) = smallest number u such that almost every number is the sum of at most u n-th powers of positive numbers. 4
1, 4, 4, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A variant of Waring's problem.

"Almost all" means that the exceptions have zero density.

Only three other values of the sequence are known: a(8) = 32, a(16) = 64, and a(32) = 128. The cited survey by Vaughan and Wooley shows that G_1(8) = 32, G_1(16) = 64, and G_1(32) = 128.  The quantity G_1(5) has not been evaluated nor has G_1(6) and G_1(7). - David Covert, Jun 29 2016

LINKS

Table of n, a(n) for n=1..4.

R. C. Vaughan and T. D. Wooley, Waring’s problem: a survey, Number Theory for the Millennium, III (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, pp. 301-340.

CROSSREFS

Cf. A002804, A079611.

Sequence in context: A326982 A263797 A331609 * A270844 A287286 A271546

Adjacent sequences:  A174403 A174404 A174405 * A174407 A174408 A174409

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane, Nov 27 2010

EXTENSIONS

a(5)-a(7) removed by David Covert, Jun 29 2016

STATUS

approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)