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A083399
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Number of divisors of n that are not divisors of other divisors of n.
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2
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1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 2, 3, 2, 3, 3, 3, 3, 4, 2, 3, 2, 3, 2, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)<=tau(n); a(n)=tau(n) iff n is prime or n=1 (A008578, A000040); a(n)=tau(n)-1 iff n is semiprime (A001358).
Number of noncomposite divisors of n. a(n) = A000005(n) - A055212(n) = A000005(n) - A033273(n) + 1. [From Jaroslav Krizek, Nov 25 2009]
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FORMULA
| a(n)=omega(n)+1, where omega=A001221.
a(n)=A010553(A007947(n))=A000005(A000005(A007947(n)))=tau_2(tau_2(rad(n))) [From Enrique Perez Herrero, Jun 25 2010]
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EXAMPLE
| {1,2,3,4,6,8,12,24} are the divisors of n=24: 1, 2, 3, 4 and 6 divide not only 24, but also 8 or 12, therefore a(24)=3.
{1,2,3,4,6,8,12,24} are the divisors of n=24: 1, 2 and 3 are noncomposites, therefore a(24)=3. [From Jaroslav Krizek, Nov 25 2009]
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MATHEMATICA
| A083399[n_Integer]:=1+PrimeNu[n]; [From Enrique Perez Herrero, Jun 25 2010]
Rest@ CoefficientList[ Series[(1/(1 - x)) + Sum[1/(1 - x^Prime[j]), {j, 200}], {x, 0, 111}], x] (* Robert G. Wilson v, Aug 16 2011 *)
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CROSSREFS
| Cf. tau=A000005.
Complement of A055212.
Sequence in context: A187186 A081147 A163671 * A105561 A087133 A196941
Adjacent sequences: A083396 A083397 A083398 * A083400 A083401 A083402
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 12 2003
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