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%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
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