A246663 Products of swinging factorials A056040.

1, 2, 4, 6, 8, 12, 16, 20, 24, 30, 32, 36, 40, 48, 60, 64, 70, 72, 80, 96, 120, 128, 140, 144, 160, 180, 192, 216, 240, 252, 256, 280, 288, 320, 360, 384, 400, 420, 432, 480, 504, 512, 560, 576, 600, 630, 640, 720, 768, 800, 840, 864, 900, 960, 1008, 1024

Offset: 1

Author

Peter Luschny, Sep 09 2014

Keywords

• nonn
• easy

Crossrefs

Cf. A001013 is a sublist.

Programs

Mathematica

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 *)

Sage

# For example prod_hull(A008578) are the natural numbers.
def prod_hull(f, K):
    S = []; newS = []
    n = 0
    while f(n) <= K:
        newS.append(f(n))
        n += 1
    while newS != S:
        S = newS; T = []
        for s in S:
            M = map(lambda n: n*s , S)
            T.extend(filter(lambda n: n <= K, M))
        newS = Set(T).union(Set(S))
    return sorted(newS)
prod_hull(lambda n: factorial(n)/factorial(n//2)^2, 1024)