A174406 a(n) = smallest number u such that almost every number is the sum of at most u n-th powers of positive numbers.

1, 4, 4, 15

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 have 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,more

Author

N. J. A. Sloane, Nov 27 2010

Extensions

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

Status

approved