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Search: id:A060431
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| A060431 |
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Number of cube-free numbers <= n. |
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+0
3
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| 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 46, 47, 47, 48, 49, 50, 51, 52, 53, 54, 54, 55, 56, 57, 58, 59, 60, 61, 61
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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I. M. Vinogradov, Elements of the Theory of Numbers,(in Russian), Moscow, 1981, p. 36.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,500
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FORMULA
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a(n)=Sum_{d>=1} mu(d)*floor(n/d^3), mu(d) = Moebius function A008683.
a(n) is asymptotic to (1/zeta(3))*n - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 13 2007
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PROGRAM
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(PARI) a(n)=sum(k=1, n, moebius(k)*floor(n/k^3)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 13 2007
(PARI) { for (n=1, 500, a=sum(k=1, n, moebius(k)*floor(n/k^3)); write("b060431.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 05 2009]
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CROSSREFS
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Cf. A013928, A013937.
Sequence in context: A157466 A097043 A053759 this_sequence A124808 A017862 A155919
Adjacent sequences: A060428 A060429 A060430 this_sequence A060432 A060433 A060434
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 06 2001
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