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A072078
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Number of 3-smooth divisors of n.
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3
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1, 2, 2, 3, 1, 4, 1, 4, 3, 2, 1, 6, 1, 2, 2, 5, 1, 6, 1, 3, 2, 2, 1, 8, 1, 2, 4, 3, 1, 4, 1, 6, 2, 2, 1, 9, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 10, 1, 2, 2, 3, 1, 8, 1, 4, 2, 2, 1, 6, 1, 2, 3, 7, 1, 4, 1, 3, 2, 2, 1, 12, 1, 2, 2, 3, 1, 4, 1, 5, 5, 2, 1, 6, 1, 2, 2, 4, 1, 6, 1, 3, 2, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = A000005(A065331(n)).
Multiplicative with a(2^e) = a(3^e) = e+1, a(p^e) = 1, p>3. Dirichlet g.f. is 2/((1-1/2^s)*(1-1/3^s)) * prod{n is a prime > 3}(1/(1-1/n^s)). Christian G. Bower (bowerc(AT)usa.net) May 20, 2005.
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FORMULA
| a(n) = (A007814(n)+1)*(A007949(n)+1).
1/Product_{k>0}(1-x^k+x^(2*k))^a(k) is g.f. for A000041(). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 07 2004
a(n)=sum_{d divides n} mu(6d)*tau(n/d) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2007
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PROG
| (PARI) a(n)=sumdiv(n, d, moebius(6*d)*numdiv(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2007
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CROSSREFS
| Cf. A000005, A003586, A072079.
Sequence in context: A089913 A059897 A071450 * A078378 A141197 A035207
Adjacent sequences: A072075 A072076 A072077 * A072079 A072080 A072081
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KEYWORD
| nonn,mult
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 13 2002
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2007
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