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A071520
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Number of 5-smooth numbers less than n.
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4
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| A 5-smooth number is a number of the form 2^x*3^y*5^z (x,y,z) >= 0.
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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 (benoit7848c(AT)orange.fr), Jun 14 2007
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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 (benoit7848c(AT)orange.fr), Jun 14 2007
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CROSSREFS
| Cf. A051037.
Cf. A112751.
Sequence in context: A086419 A025548 A121604 * A195918 A176842 A099848
Adjacent sequences: A071517 A071518 A071519 * A071521 A071522 A071523
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 02 2002
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