A071693 - OEIS

%I #33 Jan 03 2022 07:19:40

%S 1,1,2,2,4,3,5,4,6,6,7,6,9,7,10,9,11,9,12,11,13,12,13,12,17,14,16,15,

%T 17,16,19,16,19,19,20,19,24,19,21,22,25,21,26,22,26,25,26,25,29,27,28,

%U 28,29,27,33,29,33,30,31,32,37,32,34,34,37,34,38,34,38,38,39,36,43,38,40

%N Number of ways to write n as n = x*y*z + x + y + z where 0 <= x <= y <= z <= n.

%C a(n) >= floor(n / 2) + 1 = A008619(n). If x = 0 then n = x*y*z+x+y+z = y + z which has floor(n / 2) + 1 solutions. - _David A. Corneth_, Jul 31 2015

%C See A260803 for the case where 1 <= x <= y <= z. - _M. F. Hasler_, Jul 31 2015

%H David A. Corneth, <a href="/A071693/b071693.txt">Table of n, a(n) for n = 0..9999</a>  (first 1001 terms from Robert G. Wilson v)

%t mx = 100; t = 0*Range@ mx; Do[n = x*y*z + x + y + z; If[n < mx, t[[n + 1]]++], {x, 0, mx}, {y, x, mx}, {z, y, mx}]; t (* _Robert G. Wilson v_, Jul 31 2015 *)

%o (PARI) for(n=0,74,print1(sum(a=0,n,sum(b=0,a,sum(c=0,b,a*b*c+a+b+c==n)))",")) \\ _Zak Seidov_, Jul 31 2015

%o (PARI) A071693(n)=sum(x=0,n\3,sum(y=x,(n-x*(1+x^2))\2,(n-x-y)%(x*y+1)==0&&n-x>=(x*y+2)*y)) \\ _M. F. Hasler_, Jul 31 2015

%K easy,nonn

%O 0,3

%A _Benoit Cloitre_, Jun 23 2002

%E a(0) = 1 prepended by _David A. Corneth_, Jul 30 2015