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A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers).

%I A099591 #31 Feb 16 2025 08:32:55
%S A099591 47,62,63,77,78,79,127,142,143,157,158,159,207,222,223,237,238,239,
%T A099591 287,302,303,317,318,319,367,382,383,397,398,399,447,462,463,477,478,
%U A099591 479,527,542,543,557,558,559,607,622,623,687,702,703,752,767,782,783
%N A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers).
%C A099591 There are 96 members in the sequence, the largest being 13792, see the Deshouillers et al. references.
%H A099591 T. D. Noe, <a href="/A099591/b099591.txt">Table of n, a(n) for n = 1..96</a> (complete sequence)
%H A099591 J.-M. Deshouillers, F. Hennecart and B. Landreau, <a href="http://www.math.ethz.ch/EMIS/journals/JTNB/2000-2/Dhl.ps">Waring's Problem for sixteen biquadrates - numerical results</a>, Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.
%H A099591 J.-M. Deshouillers, K. Kawada and T. D. Wooley, <a href="https://doi.org/10.24033/msmf.413">On Sums of Sixteen Biquadrates</a>, Mém. Soc. Math. de France, Paris, 2005.
%H A099591 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%H A099591 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WaringsProblem.html">Warings Problem</a>
%e A099591 62 is the sum of 17 4th powers and no fewer, so 62 is a member.
%e A099591 63 is the sum of 18 4th powers and no fewer, so 63 is a member, although it is not a member of A046048.
%t A099591 f[n_] := f[n] = (k = 0; While[k++; PowersRepresentations[n, k, 4] == {}]; k); Select[Range[800], f[#] >= 17 &] (* _Jean-François Alcover_, Sep 02 2011 *)
%Y A099591 Cf. A002377, A079611, A046048.
%K A099591 nonn,fini,full,nice
%O A099591 1,1
%A A099591 _Ralf Stephan_, Oct 25 2004
%E A099591 a(25) changed from 368 to 367 by _T. D. Noe_, Sep 07 2006