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Search: id:A039960
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| A039960 |
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For n >= 2, a(n) = largest value of k such that n^k is <= n! (a(0) = a(1) = 1 by convention). |
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4
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| 1, 1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 55, 56, 57
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Seems to be slightly more than (but asymptotic to) number of nonprimes less than or equal to n.
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FORMULA
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floor[log_n(n!)]
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EXAMPLE
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a(7)=4 because 7!=5040, 7^4=2401 but 7^5=16807
a(6)=3 since 6^3.67195...=720=6! and 6^3<=6!<6^4 i.e. 216<=720<1296.
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MATHEMATICA
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ds[x_, y_] :=y!-y^x a[n_] :=Block[{m=1, s=ds[m, n]}, While[Sign[s]!=-1&&!Greater[m, 256], m++ ]; m]; Table[a[n]-1, {n, 1, 200}]//Timing Code2[transparent]: Table[Count[Part[Sign[Table[Table[n!-n^j, {j, 1, 128}], {n, 1, 128}]], u], 1], {u, 1, 128}]//Timing (from Labos)
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CROSSREFS
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a(n)=A060151(n)-1. Cf. A011776, A074181, A074182, A074184.
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KEYWORD
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nonn,new
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AUTHOR
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Dan Bentley (bentini(AT)yahoo.com)
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EXTENSIONS
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Corrected and extended by Henry Bottomley (se16(AT)btinternet.com), Mar 08 2001
Edited by njas, Sep 26 2008 at the suggestion of R. J. Mathar.
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