

A071520


Number of 5smooth numbers (A051037) <= n.


10



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



FORMULA

a(n) = Card{ k  A051037(k) <= n }.
Asymptotically : let a = 1/(6*log(2)*log(3)*log(5)) and b = sqrt(30) then a(n) = a*log(b*n)^3 + O(log(n)).
a(n) = Sum_{k=1,n} mu(30*k)*floor(n/k).  Benoit Cloitre, Jun 14 2007
a(n) = Sum_{i=0..floor(log_5(n))} Sum_{j=0..floor(log_3(n/5^i))} floor(log_2(2*n/(5^i*3^j))).  Ridouane Oudra, Jul 17 2020


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



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



