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Search: id:A065333
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| A065333 |
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Characteristic function of 3-smooth numbers, i.e. numbers of the form 2^i*3^j (i, j >= 0). |
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+0
10
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| 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = signum(A065332(n)), where signum = A057427. a(n) = if A065330(n) = 1 then 1 else 0 = 1 - signum(A065330(n) - 1).
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LINKS
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Index entries for characteristic functions
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FORMULA
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a(n) = if n = A003586(k) for some k then 1 else 0.
a(n) = Prod(0^floor(p/4): p prime and p|n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 19 2004
Multiplicative with a(2^e) = a(3^e) = 1, a(p^e) = 0 for prime p > 3. Dirichlet g.f. 1/(1-2^-s)/(1-3^-s). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 01 2006
a(n) = 0^(A038502(A000265(n)) - 1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 28 2008]
a(n)=sum(d divides n, mu(6*d)) [From Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 18 2009]
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PROGRAM
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(PARI) a(n)=sumdiv(n, d, moebius(6*d)) [From Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 18 2009]
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CROSSREFS
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Sequence in context: A115524 A117198 A054525 this_sequence A127972 A103451 A103452
Adjacent sequences: A065330 A065331 A065332 this_sequence A065334 A065335 A065336
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KEYWORD
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mult,nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 29 2001
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