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 A263292 Number of distinct values of |product(A) - product(B)| where A and B are a partition of {1,2,...,n}. 2
 1, 1, 1, 2, 4, 8, 13, 26, 44, 76, 119, 238, 324, 648, 1008, 1492, 2116, 4232, 5680, 11360, 15272, 21872, 33536, 67072, 83168, 121376, 185496, 249072, 328416, 656832, 790656, 1581312, 1980192, 2758624, 4193040, 5555616, 6532896, 13065792, 19845216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The problem of showing that no number k is equal to |product(A)-product(B)| for infinitely many different values of n appears in a Hungarian journal for high school students in math and physics (see KöMaL link). Compare to A038667, which provided the smallest value of |product(A) - product(B)|. Also the number of distinct values <= sqrt(n!) of element products of subsets of [n]. - Alois P. Heinz, Oct 17 2015 LINKS KöMaL-Mathematical and Physical Journal for Secondary Schools, Problems in Mathematics, September 2015. EXAMPLE For n = 4, the four possible values of |product(A) - product(B)| are 2, 5, 10, and 23. MAPLE b:= proc(n) option remember; local f, g, h;       if n<2 then {1}     else f, g, h:= n!, y-> `if`(y^2<=f, y, NULL), (n-1)!;          map(x-> {x, g(x*n), g(h/x)}[], b(n-1))       fi     end: a:= n-> nops(b(n)): seq(a(n), n=0..25);  # Alois P. Heinz, Oct 17 2015 MATHEMATICA a[n_] := Block[{v = Times @@@ Subsets[ Range[2, n], Floor[n/2]]}, Length@ Union@ Abs[v - n!/v]]; Array[a, 20] (* Giovanni Resta, Oct 17 2015 *) CROSSREFS Cf. A038667. Sequence in context: A043816 A048328 A094767 * A026643 A288925 A018285 Adjacent sequences:  A263289 A263290 A263291 * A263293 A263294 A263295 KEYWORD nonn AUTHOR Jerrold Grossman, Oct 13 2015 EXTENSIONS a(21)-a(27) from Giovanni Resta, Oct 17 2015 a(28)-a(38) from Alois P. Heinz, Oct 17 2015 STATUS approved

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Last modified August 7 15:08 EDT 2020. Contains 336276 sequences. (Running on oeis4.)