cp's OEIS Frontend

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

%I A084355 #10 Feb 25 2015 23:32:58
%S A084355 1,1,2,6,3,5,5,4,4,3,3,3,3,4,3,3,3,3,3,3,3
%N A084355 Least number of positive cubes needed to represent n!.
%F A084355 a(n)=A002376(n!).
%e A084355 a(4)=3 because 4!=24=2^3+2^3+2^3.
%e A084355 a(0)=1 because 0!=1=1^3.
%e A084355 a(1)=1 because 1!=1=1^3.
%e A084355 a(2)=2 because 2!=2=1^3+1^3.
%e A084355 a(3)=6 because 3!=6=1^3+1^3+1^3+1^3+1^3+1^3.
%e A084355 a(4)=3 because 4!=24=2^3+2^3+2^3.
%e A084355 a(5)=5 because 5!=120=1^3+3^3+3^3+4^3+1^3.
%e A084355 a(6)=5 because 6!=720=4^3+6^3+6^3+6^3+2^3.
%e A084355 a(7)=4 because 7!=5040=1^3+5^3+17^3+1^3.
%e A084355 a(8)=4 because 8!=40320=2^3+10^3+34^3+2^3.
%e A084355 a(9)=3 because 9!=362880=52^3+56^3+36^3.
%e A084355 a(10)=3 because 10!=3628800=96^3+140^3+4^3.
%e A084355 a(11)=3 because 11!=39916800=222^3+303^3+105^3.
%e A084355 a(12)=3 because 12!=479001600=214^3+777^3+47^3.
%e A084355 a(13)=4 because 13!=6227020800=106^3+255^3+1838^3+33^3.
%e A084355 a(14)=3 because 14!=87178291200=1344^3+4392^3+312^3.
%e A084355 a(15)=3 because 15!=1307674368000=2040^3+10908^3+1092^3.
%e A084355 a(16)=3 because 16!=20922789888000=8400^3+27040^3+8240^3.
%e A084355 a(17)=3 because 17!=355687428096000=22848^3+69984^3+9984^3.
%e A084355 a(18)=3 because 18!=6402373705728000=54060^3+184080^3+18900^3.
%e A084355 From _Donovan Johnson_, May 17 2010: (Start)
%e A084355 a(19)=3 because 19!=121645100408832000=131040^3+331200^3+436320^3.
%e A084355 a(20)=3 because 20!=2432902008176640000=87490^3+1034430^3+1098440^3.
%e A084355 (End)
%o A084355 (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
%Y A084355 Cf. A000142, A002376, A002325, A003072, A003327, A003328, A003329.
%K A084355 nonn
%O A084355 0,3
%A A084355 _Hugo Pfoertner_, Jun 22 2003
%E A084355 More terms from _David W. Wilson_, Jun 23 2003
%E A084355 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2007
%E A084355 a(19)-a(20) from _Donovan Johnson_, May 17 2010