%I #10 Mar 28 2022 07:44:01

%S 16,24,32,40,45,56,60,72,73,88,81,104,101,120,108,136,129,152,129,168,

%T 157,184,141,200,185,216,178,232,213,248,188,264,241,280,226,296,269,

%U 312,222,328,297,344,273,360,325,376,237,392,353,408,321,424,381,440

%N a(n) = Sum_{k=1..8} floor(p(n, k)/p(n-1, k)), where p(n, k) = n!/( Product_{i=1..floor(n/2^k)} A004001(i) ).

%H G. C. Greubel, <a href="/A088493/b088493.txt">Table of n, a(n) for n = 2..5000</a>

%F a(n) = Sum_{k=1..8} floor(p(n, k)/p(n-1, k)), where p(n, k) = n!/( Product_{i=1..floor(n/2^k)} A004001(i) ).

%t Conway[n_]:= Conway[n]= If[n<3, 1, Conway[Conway[n-1]] +Conway[n-Conway[n-1]]];

%t f[n_, k_]:= f[n, k]= Product[Conway[i], {i, Floor[n/2^k]}];

%t a[n_]:= a[n]= Sum[Floor[n*f[n-1,k]/f[n,k]], {k,8}];

%t Table[a[n], {n, 2, 70}] (* modified by _G. C. Greubel_, Mar 27 2022 *)

%o (Sage)

%o @CachedFunction

%o def b(n): # A004001

%o if (n<3): return 1

%o else: return b(b(n-1)) + b(n-b(n-1))

%o def f(n,k): return product( b(j) for j in (1..(n//2^k)) )

%o def A088493(n): return sum( (n*f(n-1,k)//f(n,k)) for k in (1..8) )

%o [A088493(n) for n in (2..70)] # _G. C. Greubel_, Mar 27 2022

%Y Cf. A004001, A005185, A005229, A088491.

%K nonn

%O 2,1

%A _Roger L. Bagula_, Nov 10 2003

%E Edited by _G. C. Greubel_, Mar 27 2022