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Search: id:A073311
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| A073311 |
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Number of square-free numbers in the reduced residue system of n. |
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3
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| 1, 1, 2, 2, 3, 2, 5, 4, 4, 3, 7, 4, 8, 5, 6, 7, 11, 6, 12, 7, 8, 9, 15, 8, 13, 10, 13, 9, 17, 8, 19, 13, 13, 13, 15, 11, 23, 15, 17, 14, 26, 11, 28, 17, 18, 18, 30, 15, 26, 17, 21, 19, 32, 16, 25, 20, 23, 23, 36, 15, 37, 25, 26, 26, 30, 18, 41, 26, 29, 22, 44, 22, 45, 30, 29, 29, 36
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Number of positive square-free numbers <= n that are relatively prime to n.
a(n) + A073312(n) = A000010(n).
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LINKS
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S. R. Finch, Unitarism and infinitarism.
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FORMULA
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Let s(n) = Sum_{k=1..n} a(k). Then s(n) is asymptotic to C*n^2 where C = (3/pi^2)*alpha and alpha = prod ( 1 - 1/(p*(p+1) ) = 0.7044422009... [From discussions in Number Theory List, Apr 06 2004]
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EXAMPLE
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n=15, there are A000005(15)=8 residues: 1, 2, 4=2^2, 7, 8=2^3, 11, 13 and 14; six of them are square-free: 1, 2, 7, 11, 13 and 14, therefore a(15)=6.
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CROSSREFS
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Cf. A073312, A005117, A000010, A048864, A048865.
Sequence in context: A051664 A029656 A121306 this_sequence A003974 A065769 A113298
Adjacent sequences: A073308 A073309 A073310 this_sequence A073312 A073313 A073314
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 25 2002
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