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Search: id:A071521
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| A071521 |
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Number of 3-smooth numbers <= n. |
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+0
7
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| 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A 3-smooth number is a number of the form 2^x*3^y (x,y) >= 0.
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REFERENCES
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Bruce C. Berndt and Robert A. Rankin, "Ramanujan : letters and commentary", History of Mathematics Volume 9, AMS-LMS, p. 23, p. 35
M. Haussman and H. N. Shapiro,"On Ramanujan right triangle conjecture", Comm. Pure Appl. Math. 42 (1989), 885-889
A. M. Ostrowski, "Bemerkungen zur Theorie der Diophantischen Approximationen", Abh. Math. Sem. Univ. Hamburg 1 (1922), 77-98; 250-251.
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FORMULA
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a(n) = Card{ k | A003586(k) <= n } Asymptotically : let a=1/(2log(2)log(3)) b=sqrt(6) then from Ramanujan a(n) ~ alog(2n)log(3n) or equivalently a(n) ~ alog(bn)^2
A022331(n) = a(A000079(n)); A022330(n) = a(A000244(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 09 2006
a(n)=sum(k=1,n,mu(6k)*floor(n/k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2007
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PROGRAM
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(PARI) for(n=1, 100, print1(sum(k=1, n, if(sum(i=3, n, if(k%prime(i), 0, 1)), 0, 1)), ", "))
(PARI) a(n)=sum(k=1, n, moebius(2*3*k)*floor(n/k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2007
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CROSSREFS
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Cf. A003586.
Sequence in context: A047784 A047742 A050292 this_sequence A039733 A005374 A071991
Adjacent sequences: A071518 A071519 A071520 this_sequence A071522 A071523 A071524
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 02 2002
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