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A074816
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a(n) = sum(d|n, tau(d)*mu(d)^2 ).
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4
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1, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3, 9, 3, 9, 9, 3, 3, 9, 3, 9, 9, 9, 3, 9, 3, 9, 3, 9, 3, 27, 3, 3, 9, 9, 9, 9, 3, 9, 9, 9, 3, 27, 3, 9, 9, 9, 3, 9, 3, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 27, 3, 9, 9, 3, 9, 27, 3, 9, 9, 27, 3, 9, 3, 9, 9, 9, 9, 27, 3, 9, 3, 9, 3, 27, 9, 9, 9, 9, 3, 27, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Terms are powers of 3.
The inverse Mobius transform of A074823, as the Dirichlet g.f. is product_{primes p} (1+2*p^(-s)) and the Dirichlet g.f. of A074816 is product_{primes p} (1+2*p^(-s))/(1-p^(-s)). - R. J. Mathar, Feb 09 2011
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LINKS
| R. Zumkeller, Table = of n, a(n) for n = 1..10000
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FORMULA
| a(n)=3^m if n is divisible by m distinct primes. i.e. a(n)=3 if n is in A000961; a(n)=9 if n is in A007774 ...
a(n) = 3^A001221(n) = 3^omega(n). Multiplicative with a(p^e)=3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 09 2002.
a(n)=tau_3(rad(n))=A007425(A007947(n)) - Enrique Perez Herrero (psychgeometry(AT)gmail.com), Jun 24 2010
a(n)=abs(sum(d|n, A000005(d^3)*mu(d))) [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Jun 28 2010]
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MATHEMATICA
| A074816[n_]:=3^PrimeNu[n]; [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Jun 28 2010
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CROSSREFS
| Cf. A001221, A034444, A124508.
Sequence in context: A078229 A007428 A184099 * A203564 A111575 A161836
Adjacent sequences: A074813 A074814 A074815 * A074817 A074818 A074819
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KEYWORD
| nonn,mult
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 08 2002
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