0,3

a(n)=A002376(n!).

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.

(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

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

Sequence in context: A123733 A130108 A026203 this_sequence A093650 A064433 A139384

Adjacent sequences: A084352 A084353 A084354 this_sequence A084356 A084357 A084358

nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 22 2003

More terms from David W. Wilson, Jun 23, 2003

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