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%I #31 Dec 18 2023 08:26:20
%S 1,4,4,15
%N a(n) = smallest number u such that almost every number is the sum of at most u n-th powers of positive numbers.
%C A variant of Waring's problem.
%C "Almost all" means that the exceptions have zero density.
%C 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
%H R. C. Vaughan and T. D. Wooley, <a href="https://personal.science.psu.edu/rcv4/Waring.pdf">Waring’s problem: a survey</a>, Number Theory for the Millennium, III (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, pp. 301-340.
%Y Cf. A002804, A079611.
%K nonn,hard,more
%O 1,2
%A _N. J. A. Sloane_, Nov 27 2010
%E a(5)-a(7) removed by _David Covert_, Jun 29 2016