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Search: id:A083399
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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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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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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 (jaroslav.krizek(AT)atlas.cz), Nov 25 2009]
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FORMULA
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a(n)=omega(n)+1, where omega=A001221.
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EXAMPLE
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{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 (jaroslav.krizek(AT)atlas.cz), Nov 25 2009]
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CROSSREFS
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Cf. tau=A000005.
Complement of A055212.
Sequence in context: A094915 A081147 A163671 this_sequence A105561 A087133 A062843
Adjacent sequences: A083396 A083397 A083398 this_sequence A083400 A083401 A083402
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KEYWORD
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nonn,new
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 12 2003
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