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Search: id:A096123
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| A096123 |
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Least product n*(n-1)*(n-2)*...*(n-k+1) divisible by (n-k)!. |
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+0
4
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| 1, 2, 6, 12, 60, 120, 840, 1680, 15120, 5040, 55440, 665280, 8648640, 17297280, 259459200, 518918400, 8821612800, 17643225600, 335221286400, 670442572800, 14079294028800, 28158588057600, 647647525324800, 1295295050649600
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: a(n) = n!/(p-1)! for all sufficiently large n, where p is the least prime such that n <= 2*p (Amarnath Murthy). A096974 gives numbers n such that a(n) = n!/(nextprime(n/2)-1)! and indicates that this conjecture is most probably false.
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EXAMPLE
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a(10) = 5040 as 10*9 is not divisible by 8!, 10*9*8 is not divisible by 7! but 10*9*8*7 = 5040 is divisible by 6! = 720.
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PROGRAM
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(PARI) {for(n=1, 24, p=1; k=0; b=1; while(b&&k<n, p=p*(n-k); d=(n-k)!; if(p%d==0, b=0; print1(p, ", "), k++)))}
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CROSSREFS
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Cf. A056042, A096974.
Adjacent sequences: A096120 A096121 A096122 this_sequence A096124 A096125 A096126
Sequence in context: A004490 A135060 A072486 this_sequence A081125 A138570 A161887
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 01 2004
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 17 2004
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