

A071520


Number of 5smooth numbers less than n.


5



1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 14, 14, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28
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OFFSET

1,2


COMMENTS

A 5smooth number is a number of the form 2^x*3^y*5^z (x,y,z) >= 0.


LINKS

Table of n, a(n) for n=1..73.


FORMULA

a(n) = Card{ k  A051037(k) <= n } Asymptotically : let a=1/(6log(2)log(3)log(5)) b=sqrt(30) then a(n)=alog(bn)^3 + 0(log(n))
a(n)=sum(k=1,n,mu(30k)*floor(n/k))  Benoit Cloitre, Jun 14 2007


PROG

(PARI) for(n=1, 100, print1(sum(k=1, n, if(sum(i=4, n, if(k%prime(i), 0, 1)), 0, 1)), ", "))
(PARI) a(n)=sum(k=1, n, moebius(2*3*5*k)*floor(n/k))  Benoit Cloitre, Jun 14 2007


CROSSREFS

Cf. A051037.
Cf. A112751.
Sequence in context: A287354 A025548 A121604 * A195918 A176842 A278055
Adjacent sequences: A071517 A071518 A071519 * A071521 A071522 A071523


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jun 02 2002


STATUS

approved



