

A064775


Card{ k<=n, k such that all prime divisors of k are <= sqrt(k) }.


1



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
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OFFSET

1,4


COMMENTS

A048098(n) is the nth number k such that all prime divisors of k are <= sqrt(k).


REFERENCES

D. P. Parent, Exercices de theorie des nombres, Les grands classiques, GauthierVillars, Edition Jacques Gabay, p. 17


LINKS

Harry J. Smith, Table of n, a(n) for n=1..1000


FORMULA

a(n)=nsum(p<=sqrt(n), (p1))sum(sqrt(n)<p<=n, floor(n/p)). a(n) is the largest k such that A048098(k)<=n. Asymptotically: a(n)=(1log(2))*n + O(n/log(n)).


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.


PROG

(PARI) a(n)=nsum(k=1, floor(sqrt(n)+10^20), (k1)*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), (k1)*isprime(k))  sum(k=ceil(sqrt(n) + 10^20), n, floor(n/k)*isprime(k)); write("b064775.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 24 2009


CROSSREFS

Cf. A048098.
Sequence in context: A025779 A085003 A119026 * A260731 A194239 A064475
Adjacent sequences: A064772 A064773 A064774 * A064776 A064777 A064778


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, May 11 2002


STATUS

approved



