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A200744 Divide integers 1..n into two sets, minimizing the difference of their products. This sequence is the larger product. 3
1, 2, 3, 6, 12, 30, 72, 210, 630, 1920, 6336, 22176, 79200, 295680, 1146600, 4586400, 18869760, 80061696, 348986880, 1560176640, 7148445696, 33530112000, 160825785120, 787718131200, 3938590656000, 20083261440000, 104351247000000, 552173794099200, 2973528918360000, 16286983961149440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

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.

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 (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])); ll[n]/ g(1, nops(l), 1) end: seq(a(n), n=1..23);  # Alois P. Heinz, Nov 22 2011

CROSSREFS

Cf. A061056, A060777, A200743, A038667.

Sequence in context: A014278 A061056 A060777 * A089430 A213242 A243299

Adjacent sequences:  A200741 A200742 A200743 * A200745 A200746 A200747

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Nov 21 2011

EXTENSIONS

a(24)-a(30) from Alois P. Heinz, Nov 22 2011

STATUS

approved

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Last modified November 14 00:05 EST 2019. Contains 329106 sequences. (Running on oeis4.)