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A064775
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Card{ k<=n, k such that all prime divisors of k are <= sqrt(k) }.
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1
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1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 16, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 23, 23, 23, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| A048098(n) is the n-th number k such that all prime divisors of k are <= sqrt(k).
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REFERENCES
| D. P. Parent, Exercices de theorie des nombres, Les grands classiques, Gauthier-Villars, Edition Jacques Gabay, p. 17
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| a(n)=n-sum(p<=sqrt(n), (p-1))-sum(sqrt(n)<p<=n, floor(n/p)). a(n) is the largest k such that A048098(k)<=n. Asymptotically: a(n)=(1-ln(2))*n + O(n/ln(n)).
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EXAMPLE
| Below 28, only k=27,25,24,18,16,12,9,8,4,1 have all their prime divisors less than or equal to sqrt(k), hence a(28)=10. To obtain from A048098(n): A048098(10)=27<=28 < A048098(11)=30, hence a(28)=10.
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PROG
| (PARI) a(n)=n-sum(k=1, floor(sqrt(n)+10^-20), (k-1)*isprime(k))-sum(k=ceil(sqrt(n)+10^-20), n, floor(n/k)*isprime(k))
(PARI) { for (n=1, 1000, a=n - sum(k=1, floor(sqrt(n) + 10^-20), (k-1)*isprime(k)) - sum(k=ceil(sqrt(n) + 10^-20), n, floor(n/k)*isprime(k)); write("b064775.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 24 2009]
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CROSSREFS
| Cf. A048098.
Sequence in context: A025779 A085003 A119026 * A194239 A064475 A025774
Adjacent sequences: A064772 A064773 A064774 * A064776 A064777 A064778
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 11 2002
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