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 A200743 Divide integers 1..n into two sets, minimizing the difference of their products. This sequence is the smaller product. 4
 1, 1, 2, 4, 10, 24, 70, 192, 576, 1890, 6300, 21600, 78624, 294840, 1140480, 4561920, 18849600, 79968000, 348566400, 1559376000, 7147140000, 33522128640, 160745472000, 787652812800, 3938264064000, 20080974513600, 104348244639744, 552160113120000, 2973491173785600, 16286186592000000, 90678987245246400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..35 EXAMPLE For n=1, we put 1 in one set and the other is empty; with the standard convention for empty products, both products are 1. For n=13, the central pair of divisors of n! are 78975 and 78848. Since neither is divisible by 10, these values cannot be obtained. The next pair of divisors are 79200 = 12*11*10*6*5*2*1 and 78624 = 13*9*8*7*4*3, so a(13) = 78624. MAPLE a:= proc(n) local l, ll, g, p, i; l:= [i\$i=1..n]; ll:= [i!\$i=1..n]; g:= proc(m, j, b) local mm, bb, k; if j=1 then m else mm:= m; bb:= b; for k to 2 while (mmbb then bb:= max(bb, g(mm, j-1, bb)) fi; mm:= mm*l[j] od; bb fi end; Digits:= 700; p:= ceil(sqrt(ll[n])); g(1, nops(l), 1) end: seq(a(n), n=1..23);  # Alois P. Heinz, Nov 22 2011 MATHEMATICA a[n_] := a[n] = Module[{s, t}, {s, t} = MinimalBy[{#, Complement[Range[n], #]}& /@ Subsets[Range[n]], Abs[Times @@ #[[1]] - Times @@ #[[2]]]&][[1]]; Min[Times @@ s, Times @@ t]]; Table[Print[n, " ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Nov 03 2020 *) PROG (Python) from itertools import combinations def prod(l):     t=1     for x in l:         t *= x     return t def a200743(n):     nums = list(range(1, n+1))     widths = combinations(nums, n//2)     dimensions = [(prod(width), prod(x for x in nums if x not in width)) for width in widths]     best = min(dimensions, key=lambda x:max(*x)-min(*x))     return min(best) # Christian Perfect, Feb 04 2015 CROSSREFS Cf. A061055, A060776, A200744, A038667. Sequence in context: A028506 A029893 A148089 * A060776 A061055 A148090 Adjacent sequences:  A200740 A200741 A200742 * A200744 A200745 A200746 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Nov 21 2011 EXTENSIONS a(24)-a(30) from Alois P. Heinz, Nov 22 2011 a(31) from Michael S. Branicky, May 21 2021 STATUS approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)