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Search: id:A068819
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| A068819 |
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n!/((n+1)*(n+2)*...*(n+k)) where k is largest value that gives an integer quotient. |
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+0
1
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| 1, 2, 6, 24, 20, 720, 7, 448, 36288, 3628800, 3326400, 479001600, 1853280, 363242880, 81729648000, 20922789888000, 19760412672000, 6402373705728000, 13165054156800, 5266021662720000, 2322315553259520000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n! is divisible by all the numbers from n+1 to n+k where n+k+1 is the smallest prime greater than n. Conjecture: For n > 3 n! is divisible by Product(n+k,n)= (n+1)(n+2)...(n+k).
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REFERENCES
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Amarnath Murthy, Smarandache Reciprocal function and an elementary inquality. Smarndache Notions Journal Vol. 11, 2000.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
M. L. Perez et al., eds., Smarandache Notions Journal
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FORMULA
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a(n) = smallest integer value of (n!)^2/(n+k)! i.e. n+k+1 does not divide a(n).
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EXAMPLE
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a(7)= 7 as 5040/8 = 630, 630/9 = 70, 70/10 = 7 but 7 is not divisible by 11.
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CROSSREFS
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Sequence in context: A004154 A076126 A124900 this_sequence A060068 A099732 A118381
Adjacent sequences: A068816 A068817 A068818 this_sequence A068820 A068821 A068822
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 08 2002
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EXTENSIONS
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Corrected by T. D. Noe, May 08 2007
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