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Search: id:A112929
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| A112929 |
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Number of squarefree integers not exceeding the n-th prime. |
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+0
6
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| 1, 2, 3, 5, 7, 8, 11, 12, 15, 17, 19, 23, 26, 28, 30, 32, 36, 37, 41, 44, 45, 49, 51, 55, 60, 61, 63, 66, 67, 70, 77, 80, 83, 85, 91, 92, 95, 99, 102, 104, 108, 109, 116, 117, 120, 121, 129, 138, 140, 141, 144, 148, 149, 153, 157, 161, 165, 166, 169, 171, 173, 179, 187
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = order of n-th term of A112925 among squarefree integers.
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LINKS
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Diana Mecum, Table of n, a(n) for n = 1..200
Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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A005117(a(n)) = A112925(n). - R. J. Mathar, Apr 19 2008
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EXAMPLE
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a(5)=7 because the 5th prime is 11 and the squarefree numbers not exceeding 11 are: 2,3,5,6,7,10,11.
The 5th term of A112925 is 10 and 10 is the 7th squarefree integer (with 1 counted as the first squarefree integer). So a(5) = 7.
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MAPLE
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with(numtheory): a:=proc(n) local p, B, j: p:=ithprime(n): B:={}: for j from 2 to p do if abs(mobius(j))>0 then B:=B union {j} else B:=B fi od: nops(B) end: seq(a(m), m=1..75);
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MATHEMATICA
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f[n_] := Prime[n] - Sum[ If[ MoebiusMu[k]]==0, 1, 0], {k, Prime[n]}] - 1; Table[ f[n], {n, 63}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 15 2005)
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CROSSREFS
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Cf. A112925, A112926, A061400, A112928, A112930.
Sequence in context: A066680 A028780 A083028 this_sequence A099519 A014121 A051600
Adjacent sequences: A112926 A112927 A112928 this_sequence A112930 A112931 A112932
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Oct 06 2005 and Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2005
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EXTENSIONS
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More terms from Diana Mecum (diana.mecum(AT)gmail.com), May 29 2007
Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 26 2008 at the suggestion of R. J. Mathar.
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