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Search: id:A073184
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| A073184 |
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Number of cube-free divisors of n. |
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+0
4
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| 1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 3, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 3, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 6, 3, 4, 2, 12, 4, 4, 4, 6, 2, 12, 4, 6, 4, 4, 4, 6, 2, 6, 6, 9, 2, 8, 2
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OFFSET
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1,2
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COMMENT
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a(n) = sum of divisors of the cube-free kernel of n: a(n)=A073184(A007948(n));
a(n) <= A073182(n).
Multiplicative because it is the Inverse Moebius transform of the characteristic function of cube-free numbers. a(n) is a prime signature sequence. a(p) = 2, a(p^e) = 3, e>1. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
Multiplicative because it is the Dirichlet convolution of a(n)=n with characteristic function of cube-free numbers, both multiplicative sequences. a(p) = 1+p, a(p^e) = 1+p+p^2, e>1. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
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EXAMPLE
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The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, 8=2^3 and 56=7*2^3 are not cube-free, therefore a(56)=6.
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CROSSREFS
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Cf. A000005, A073185, A004709, A073183, A073180, A034444.
Sequence in context: A111336 A083902 A106491 this_sequence A073182 A049599 A043261
Adjacent sequences: A073181 A073182 A073183 this_sequence A073185 A073186 A073187
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KEYWORD
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nonn,mult
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 19 2002
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