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Search: id:A055377
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| A055377 |
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a(n) = largest prime <= [n/2]. |
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+0
1
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| 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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Also largest prime factor of any composite <= n. E.g. a(15) = 7 since 7 is the largest prime factor of {4,6,8,9,10,12,14,15}, the composites <= 15.
Also largest prime dividing A025527(n) = n!/LCM[1,..,n]. [Comment from Ray Chandler, Apr 26 2007: Primes > n/2 don't appear as factors of A025507(n) since they appear once in n! and again in the denominator LCM[1,...,n]. Primes <= n/2 appear more times in the numerator than the denominator so they appear in the fraction.]
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FORMULA
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a(n) = Max(gpf((n+2) mod k): 1<k<(n+2) and k not prime), with gpf=A006530 (greatest prime factor). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 27 2004
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EXAMPLE
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n = 10, n! = 3628800, LCM[1,..,10] = 2520, A025527(10) = 1440 = 32.9.5 so a(7) = 5 (offset = 3)
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CROSSREFS
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Cf. A000142, A003418, A025527, A007917.
Sequence in context: A048280 A024695 A124229 this_sequence A128586 A130971 A051776
Adjacent sequences: A055374 A055375 A055376 this_sequence A055378 A055379 A055380
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 22 2000; David W. Wilson (davidwwilson(AT)comcast.net), Jun 10 2005
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
Edited by njas at the suggestion of Andrew Plewe, May 14 2007
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