

A099591


Numbers that are the sum of no fewer than 17 biquadrates (4th powers).


10



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
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OFFSET

1,1


COMMENTS

There are 96 members in the sequence, the largest being 13792, see the Deshouillers et al. references.


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. 411422.
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


EXAMPLE

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.


MATHEMATICA

f[n_] := f[n] = (k = 0; While[k++; PowersRepresentations[n, k, 4] == {}]; k); Select[Range[800], f[#] >= 17 &] (* JeanFrançois Alcover, Sep 02 2011 *)


CROSSREFS

Cf. A002377, A079611, A046048.
Sequence in context: A039355 A043178 A043958 * A046048 A163390 A023303
Adjacent sequences: A099588 A099589 A099590 * A099592 A099593 A099594


KEYWORD

nonn,fini,full,nice


AUTHOR

Ralf Stephan, Oct 25 2004


EXTENSIONS

a(25) changed from 368 to 367 by T. D. Noe, Sep 07 2006


STATUS

approved



