

A085304


Least number of 4th powers required to represent n!.


0



1, 1, 2, 6, 9, 10, 15, 15, 9, 10, 15, 6, 12, 12
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..13.
Eric Weisstein's World of Mathematics, Biquadratic Number


FORMULA

"Shortest" solutions to n!=Sum[x(j)^4], j=1, .., m[n] with minimal value of m[n]: a(n)=Min{m[n]}. Per analogiam A084355.


EXAMPLE

n=6: 6!=720=625+81+14,lengthofsolution=16>=a(6)
but 6!=720=2.256+13.16 seems shortest solution a(6)=15
after, see also A046046
n=7: 7!=5040=3.1296+4.256+8.16 so a(7)<=15 (uncertain);
n=8: a(8)<=9 because 8!=4.10000+1.256+4.16.


CROSSREFS

Cf. A000142, A084355, A060387, A003336A003346, A046046, A046044A046050.
Sequence in context: A276936 A276937 A243373 * A015843 A109600 A071814
Adjacent sequences: A085301 A085302 A085303 * A085305 A085306 A085307


KEYWORD

more,nonn


AUTHOR

Labos Elemer, Jun 30 2003


EXTENSIONS

a(7)a(11) from John W. Layman, Aug 13 2004
a(12) from Sean A. Irvine, Feb 11 2010
a(13) from Sean A. Irvine, Feb 15 2010


STATUS

approved



