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A071520 Number of 5-smooth 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A 5-smooth 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
Sequence in context: A287354 A025548 A121604 * A195918 A371156 A176842
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 02 2002
EXTENSIONS
Title corrected by Rainer Rosenthal, Aug 30 2020
STATUS
approved

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Last modified June 12 10:07 EDT 2024. Contains 373329 sequences. (Running on oeis4.)