cp's OEIS Frontend

A088493 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) ).

%I A088493 #10 Mar 28 2022 07:44:01
%S A088493 16,24,32,40,45,56,60,72,73,88,81,104,101,120,108,136,129,152,129,168,
%T A088493 157,184,141,200,185,216,178,232,213,248,188,264,241,280,226,296,269,
%U A088493 312,222,328,297,344,273,360,325,376,237,392,353,408,321,424,381,440
%N A088493 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 A088493 G. C. Greubel, <a href="/A088493/b088493.txt">Table of n, a(n) for n = 2..5000</a>
%F A088493 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 A088493 Conway[n_]:= Conway[n]= If[n<3, 1, Conway[Conway[n-1]] +Conway[n-Conway[n-1]]];
%t A088493 f[n_, k_]:= f[n, k]= Product[Conway[i], {i, Floor[n/2^k]}];
%t A088493 a[n_]:= a[n]= Sum[Floor[n*f[n-1,k]/f[n,k]], {k,8}];
%t A088493 Table[a[n], {n, 2, 70}] (* modified by _G. C. Greubel_, Mar 27 2022 *)
%o A088493 (Sage)
%o A088493 @CachedFunction
%o A088493 def b(n): # A004001
%o A088493     if (n<3): return 1
%o A088493     else: return b(b(n-1)) + b(n-b(n-1))
%o A088493 def f(n,k): return product( b(j) for j in (1..(n//2^k)) )
%o A088493 def A088493(n): return sum( (n*f(n-1,k)//f(n,k)) for k in (1..8) )
%o A088493 [A088493(n) for n in (2..70)] # _G. C. Greubel_, Mar 27 2022
%Y A088493 Cf. A004001, A005185, A005229, A088491.
%K A088493 nonn
%O A088493 2,1
%A A088493 _Roger L. Bagula_, Nov 10 2003
%E A088493 Edited by _G. C. Greubel_, Mar 27 2022