A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers).
47, 62, 63, 77, 78, 79, 127, 142, 143, 157, 158, 159, 207, 222, 223, 237, 238, 239, 287, 302, 303, 317, 318, 319, 367, 382, 383, 397, 398, 399, 447, 462, 463, 477, 478, 479, 527, 542, 543, 557, 558, 559, 607, 622, 623, 687, 702, 703, 752, 767, 782, 783
Offset: 1
Examples
62 is the sum of 17 4th powers and no fewer, so 62 is a member. 63 is the sum of 18 4th powers and no fewer, so 63 is a member, although it is not a member of A046048.
Links
- T. D. Noe, Table of n, a(n) for n = 1..96 (complete sequence)
- J.-M. Deshouillers, F. Hennecart and B. Landreau, Waring's Problem for sixteen biquadrates - numerical results, Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.
- J.-M. Deshouillers, K. Kawada and T. D. Wooley, On Sums of Sixteen Biquadrates, Mém. Soc. Math. de France, Paris, 2005.
- Eric Weisstein's World of Mathematics, Biquadratic Number
- Eric Weisstein's World of Mathematics, Warings Problem
Programs
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Mathematica
f[n_] := f[n] = (k = 0; While[k++; PowersRepresentations[n, k, 4] == {}]; k); Select[Range[800], f[#] >= 17 &] (* Jean-François Alcover, Sep 02 2011 *)
Extensions
a(25) changed from 368 to 367 by T. D. Noe, Sep 07 2006
Comments