A084355 Least number of positive cubes needed to represent n!.

1, 1, 2, 6, 3, 5, 5, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=A002376(n!).

Example

a(4)=3 because 4!=24=2^3+2^3+2^3.
a(0)=1 because 0!=1=1^3.
a(1)=1 because 1!=1=1^3.
a(2)=2 because 2!=2=1^3+1^3.
a(3)=6 because 3!=6=1^3+1^3+1^3+1^3+1^3+1^3.
a(4)=3 because 4!=24=2^3+2^3+2^3.
a(5)=5 because 5!=120=1^3+3^3+3^3+4^3+1^3.
a(6)=5 because 6!=720=4^3+6^3+6^3+6^3+2^3.
a(7)=4 because 7!=5040=1^3+5^3+17^3+1^3.
a(8)=4 because 8!=40320=2^3+10^3+34^3+2^3.
a(9)=3 because 9!=362880=52^3+56^3+36^3.
a(10)=3 because 10!=3628800=96^3+140^3+4^3.
a(11)=3 because 11!=39916800=222^3+303^3+105^3.
a(12)=3 because 12!=479001600=214^3+777^3+47^3.
a(13)=4 because 13!=6227020800=106^3+255^3+1838^3+33^3.
a(14)=3 because 14!=87178291200=1344^3+4392^3+312^3.
a(15)=3 because 15!=1307674368000=2040^3+10908^3+1092^3.
a(16)=3 because 16!=20922789888000=8400^3+27040^3+8240^3.
a(17)=3 because 17!=355687428096000=22848^3+69984^3+9984^3.
a(18)=3 because 18!=6402373705728000=54060^3+184080^3+18900^3.
From Donovan Johnson, May 17 2010: (Start)
a(19)=3 because 19!=121645100408832000=131040^3+331200^3+436320^3.
a(20)=3 because 20!=2432902008176640000=87490^3+1034430^3+1098440^3.
(End)

Prog

(PARI) a(n, up, dw, k)=local(i, m); if(k==1, if(n==round(sqrtn(n, 3))^3, return(1), return(-1)), forstep(i=up, dw, -1, m=n-i^3; if(a(m, min(i, floor(sqrtn(m, 3))), ceil(sqrtn(m/(k-1), 3)), k-1)==1, return(1)))) for(n=0, 18, for(k=1, 9, if(a(n!, floor(sqrtn(n!, 3)), ceil(sqrtn(n!/k, 3)), k)==1, print1(k", "); break))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2007

Crossrefs

Cf. A000142, A002376, A002325, A003072, A003327, A003328, A003329.

Sequence in context: A154048 A259018 A353649 * A093650 A064433 A163338

Adjacent sequences: A084352 A084353 A084354 * A084356 A084357 A084358

Keyword

nonn

Author

Hugo Pfoertner, Jun 22 2003

Extensions

More terms from David W. Wilson, Jun 23 2003

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2007

a(19)-a(20) from Donovan Johnson, May 17 2010

Status

approved