A085304 Least number of 4th powers required to represent n!.

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

Offset: 0

Author

Labos Elemer, Jun 30 2003

Keywords

• more
• nonn

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

Cf. A000142, A084355, A060387, A003336-A003346, A046046, A046044-A046050.

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.

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