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A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

J.-M. Deshouillers, K. Kawada and T. D. Wooley, On Sums of Sixteen Biquadrates, Soc. Math. de France, Paris, 2005.

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.

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 &] (* Jean-François 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

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Last modified February 14 02:35 EST 2016. Contains 268318 sequences.