A246663 - OEIS

%I #12 Feb 27 2020 16:49:28

%S 1,2,4,6,8,12,16,20,24,30,32,36,40,48,60,64,70,72,80,96,120,128,140,

%T 144,160,180,192,216,240,252,256,280,288,320,360,384,400,420,432,480,

%U 504,512,560,576,600,630,640,720,768,800,840,864,900,960,1008,1024

%N Products of swinging factorials A056040.

%t sw[n_] := n!/(Floor[n/2]!)^2; lim = 40; For[p = 0; a = f = Table[sw[n], {n, lim}], p =!= a, p = a; a = Select[Union@@Outer[Times, f, a], #<= sw[lim]&]]; a (* _Hans Havermann_, Sep 09 2014 *)

%o (Sage)

%o # For example prod_hull(A008578) are the natural numbers.

%o def prod_hull(f, K):

%o     S = []; newS = []

%o     n = 0

%o     while f(n) <= K:

%o         newS.append(f(n))

%o         n += 1

%o     while newS != S:

%o         S = newS; T = []

%o         for s in S:

%o             M = map(lambda n: n*s , S)

%o             T.extend(filter(lambda n: n <= K, M))

%o         newS = Set(T).union(Set(S))

%o     return sorted(newS)

%o prod_hull(lambda n: factorial(n)/factorial(n//2)^2, 1024)

%Y Cf. A001013 is a sublist.

%K nonn,easy

%O 1,2

%A _Peter Luschny_, Sep 09 2014