Search: id:A064775
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%I A064775
%S A064775 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,
%T A064775 12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,16,17,18,18,18,18,19,19,
%U A064775 20,20,20,20,21,21,21,22,23,23,23,23,23,23,24,24,25,25,25,26,26,26,26
%N A064775 Card{ k<=n, k such that all prime divisors of k are <= sqrt(k) }.
%C A064775 A048098(n) is the n-th number k such that all prime divisors of k are 
               <= sqrt(k).
%D A064775 D. P. Parent, Exercices de theorie des nombres, Les grands classiques, 
               Gauthier-Villars, Edition Jacques Gabay, p. 17
%H A064775 Harry J. Smith, <a href="b064775.txt">Table of n, a(n) for n=1,...,1000</
               a>
%F A064775 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)).
%e A064775 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.
%o A064775 (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))
%o A064775 (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]
%Y A064775 Cf. A048098.
%Y A064775 Sequence in context: A025779 A085003 A119026 this_sequence A064475 A025774 
               A001156
%Y A064775 Adjacent sequences: A064772 A064773 A064774 this_sequence A064776 A064777 
               A064778
%K A064775 easy,nonn
%O A064775 1,4
%A A064775 Benoit Cloitre (benoit7848c(AT)orange.fr), May 11 2002

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