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Search: id:A048865
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| A048865 |
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Number of primes in the reduced residue system mod n. |
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10
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| 0, 0, 1, 1, 2, 1, 3, 3, 3, 2, 4, 3, 5, 4, 4, 5, 6, 5, 7, 6, 6, 6, 8, 7, 8, 7, 8, 7, 9, 7, 10, 10, 9, 9, 9, 9, 11, 10, 10, 10, 12, 10, 13, 12, 12, 12, 14, 13, 14, 13, 13, 13, 15, 14, 14, 14, 14, 14, 16, 14, 17, 16, 16, 17, 16, 15, 18, 17, 17, 16, 19, 18, 20, 19, 19, 19, 19, 18, 21, 20, 21
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Sum{ceil(n/p) - floor(n/p): p prime and p<=n}: a(n)=A093614(n)-A013939(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 05 2004
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FORMULA
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a(n) = A000720(n) - A001221(n)
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EXAMPLE
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At n=30 all but 1 element in reduced residue system of 30 are primes (see A048597) so a(30)=Phi(30)-1=7. n=100: a(100)=Pi(100)-A001221(100)=25-2=23.
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MATHEMATICA
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p=Prime[Range[1000]]; q=Table[PrimePi[i], {i, 1, 1000}]; t=Table[c=0; Do[If[GCD[p[[j]], i]==1, c++ ], {j, 1, q[[i-1]]}]; c, {i, 2, 950}]
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CROSSREFS
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Cf. A000010, A000720, A001221, A048597, A070296.
Sequence in context: A138022 A113278 A132382 this_sequence A058754 A125087 A111353
Adjacent sequences: A048862 A048863 A048864 this_sequence A048866 A048867 A048868
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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)
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