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A246663 Products of swinging factorials A056040.

%I A246663 #12 Feb 27 2020 16:49:28
%S A246663 1,2,4,6,8,12,16,20,24,30,32,36,40,48,60,64,70,72,80,96,120,128,140,
%T A246663 144,160,180,192,216,240,252,256,280,288,320,360,384,400,420,432,480,
%U A246663 504,512,560,576,600,630,640,720,768,800,840,864,900,960,1008,1024
%N A246663 Products of swinging factorials A056040.
%t A246663 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 A246663 (Sage)
%o A246663 # For example prod_hull(A008578) are the natural numbers.
%o A246663 def prod_hull(f, K):
%o A246663     S = []; newS = []
%o A246663     n = 0
%o A246663     while f(n) <= K:
%o A246663         newS.append(f(n))
%o A246663         n += 1
%o A246663     while newS != S:
%o A246663         S = newS; T = []
%o A246663         for s in S:
%o A246663             M = map(lambda n: n*s , S)
%o A246663             T.extend(filter(lambda n: n <= K, M))
%o A246663         newS = Set(T).union(Set(S))
%o A246663     return sorted(newS)
%o A246663 prod_hull(lambda n: factorial(n)/factorial(n//2)^2, 1024)
%Y A246663 Cf. A001013 is a sublist.
%K A246663 nonn,easy
%O A246663 1,2
%A A246663 _Peter Luschny_, Sep 09 2014