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A038667
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Minimal value of |product(A)-product(B)| where A and B are a partition of {1,2,3,...n}.
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3
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0, 1, 1, 2, 2, 6, 2, 18, 54, 30, 36, 576, 576, 840, 6120, 24480, 20160, 93696, 420480, 800640, 1305696, 7983360, 80313120, 65318400, 326592000, 2286926400, 3002360256, 13680979200, 37744574400, 797369149440, 1763653953600, 16753029012720, 16880461678080
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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) = 79200 - 78624 = 576.
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MAPLE
| a:= proc(n) local l, ll, g, gg, 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 (mm<p) do if j=2 or k=2 or k=1 and ll[j-1]*mm>bb 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])); gg:= g (1, nops(l), 1); ll[n]/gg -gg end: seq (a(n), n=1..20); # Alois P. Heinz, Jul 09 2009
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CROSSREFS
| Cf. A061057, A200743, A200744.
Sequence in context: A036655 A098792 A061057 * A199823 A013608 A196441
Adjacent sequences: A038664 A038665 A038666 * A038668 A038669 A038670
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KEYWORD
| nonn
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
| a(28)-a(31) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 09 2009
a(1) and examples from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 22 2011
a(32)-a(33) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 23 2011
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