%I #24 May 05 2024 01:46:40
%S 1,1,2,2,6,8,15,25,52,89,166,299,551,1050,1954,3737,7098,13423,25262,
%T 48028,91636,175204,334986,643526,1240052,2394026,4620984,8946603,
%U 17299096,33473294,64874632,125827199,243999584,473735230,920101286,1789429184,3482073702
%N Number of practical numbers between powers of 2 where the practical numbers are A005153.
%C a(n) appears to be a complete sequence analogous to A036378.
%e a(4) = 6 as there are 4 practical numbers > 16 and <= 32 namely 18, 20, 24, 28, 30 and 32.
%t PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Table[Length[Select[Range[2^n + 1, 2^(n + 1)], PracticalQ]],
%t {n, 0, 25}](* using _T. D. Noe_'s program A005153 *)
%Y First differences of A209237.
%Y Cf. A005153, A036378, A322257, A327824.
%K nonn
%O 0,3
%A _Frank M Jackson_, May 03 2013
%E a(26)-a(36) from _Amiram Eldar_, May 05 2024