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 A018886 Waring's problem: least positive integer requiring maximum number of terms when expressed as a sum of positive n-th powers. 1
 1, 7, 23, 79, 223, 703, 2175, 6399, 19455, 58367, 176127, 528383, 1589247, 4767743, 14319615, 42991615, 129105919, 387186687, 1161822207, 3486515199, 10458497023, 31377588223, 94136958975, 282427654143, 847282962431, 2541815332863 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = (Q-1)*(2^n) +(2^n-1)*(1^n) is a sum of Q +2^n -2 terms, Q = trunc(3^n / 2^n). REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 393 LINKS T. D. Noe, Table of n, a(n) for n=1..200 P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ex. 7.1.1. [?Broken link] P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ex. 7.1.1. Eric Weisstein's World of Mathematics, Waring's Problem. FORMULA a(n) = 2^n*[(3/2)^n] - 1 = 2^n*A002379(n) -1. EXAMPLE a(3)= 23= 16+ 7= 2*(2^3) + 7*(1^3) is a sum of 9 cubes; a(4)= 79= 64+15= 4*(2^4) +15*(1^4) is a sum of 19 biquadrates. MAPLE A018886 := proc(n) 2^n*floor((3/2)^n)-1 end proc: # R. J. Mathar, May 07 2015 MATHEMATICA a[n_]:=-1+2^n*Floor[(3/2)^n] a[Range[1, 20]] (* Julien Kluge, Jul 21 2016 *) CROSSREFS Cf. A079611. Sequence in context: A242496 A048539 A240526 * A145842 A086908 A093069 Adjacent sequences:  A018883 A018884 A018885 * A018887 A018888 A018889 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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