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A159070
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Count of numbers k in the range 1<k<= n such that set of proper divisors of k is a subset of the set of proper divisors of n.
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2
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0, 1, 2, 3, 3, 5, 4, 6, 5, 6, 5, 10, 6, 8, 8, 9, 7, 11, 8, 12, 10, 10, 9, 16, 10, 11, 11, 13, 10, 17, 11, 15, 13, 13, 13, 19, 12, 14, 14, 19, 13, 19, 14, 18, 19, 16, 15, 24, 16, 19, 17, 19, 16, 22, 18, 23, 18, 18, 17, 28, 18, 20, 23, 23, 20, 24, 19, 23, 21, 26, 20, 31, 21, 23, 25, 25
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Here proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as defined in A032741.
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FORMULA
| a(n) = A158973(n) - 1.
If p = prime, element of A000040, a(p) = A158973(p) - 1 = A036234(p) - 1 = A000720(p).
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EXAMPLE
| a(n=8) = 6 admits the following 6 k: 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with subsets of the proper divisors {1, 2, 4} for n = 8.
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CROSSREFS
| Cf.: A158973, A000040, A036234, A000720.
Sequence in context: A116922 A086898 A123031 * A088241 A163126 A088922
Adjacent sequences: A159067 A159068 A159069 * A159071 A159072 A159073
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KEYWORD
| nonn
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Apr 04 2009
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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