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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 (list; graph; refs; listen; history; text; internal format)
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,length-of-solution=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, A003336-A003346, A046046, A046044-A046050.

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

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)