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 A112929 Number of squarefree integers less than the n-th prime. 7
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = order of n-th term of A112925 among squarefree integers. a(n) = A175046(A000040(n)). - Reinhard Zumkeller, Apr 05 2010 LINKS Diana Mecum and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 200 terms from Mecum) FORMULA A005117(a(n)) = A112925(n). - R. J. Mathar, Apr 19 2008 a(n) ~ 6/Pi^2 * n log n. - Charles R Greathouse IV, Apr 26 2012 EXAMPLE 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. MAPLE 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); MATHEMATICA f[n_] := Prime[n] - Sum[ If[ MoebiusMu[k]==0, 1, 0], {k, Prime[n]}] - 1; Table[ f[n], {n, 63}] (* Robert G. Wilson v, Oct 15 2005 *) PROG (PARI) a(n)={ my(lim=prime(n)-1, b=sqrtint(lim\2)); sum(k=1, b, moebius(k)*(lim\k^2))+ sum(k=b+1, sqrt(lim), moebius(k)) }; \\ Charles R Greathouse IV, Apr 26 2012 (PARI) a(n, p=prime(n))=p--; my(s, b=sqrtint(p\2)); forsquarefree(k=1, b, s += p\k^2*moebius(k)); forsquarefree(k=b+1, sqrtint(p), s += moebius(k)); s \\ Charles R Greathouse IV, Jan 08 2018 CROSSREFS Cf. A112925, A112926, A061400, A112928, A112930. Sequence in context: A288625 A189168 A182799 * A242324 A099519 A014121 Adjacent sequences:  A112926 A112927 A112928 * A112930 A112931 A112932 KEYWORD nonn AUTHOR Leroy Quet, Oct 06 2005 and Emeric Deutsch, Oct 14 2005 EXTENSIONS More terms from Diana L. Mecum, May 29 2007 Edited by N. J. A. Sloane, Apr 26 2008 at the suggestion of R. J. Mathar Mathematica syntax corrected by Frank M Jackson, Dec 28 2018 STATUS approved

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Last modified May 14 12:37 EDT 2021. Contains 343884 sequences. (Running on oeis4.)