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A159072
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Count of numbers k in the range 1<=k<= n such that set of proper divisors of k is not a subset of the set of the proper divisors of n.
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1
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1, 1, 1, 1, 2, 1, 3, 2, 4, 4, 6, 2, 7, 6, 7, 7, 10, 7, 11, 8, 11, 12, 14, 8, 15, 15, 16, 15, 19, 13, 20, 17, 20, 21, 22, 17, 25, 24, 25, 21, 28, 23, 29, 26, 26, 30, 32, 24, 33, 31, 34, 33, 37, 32, 37, 33, 39, 40, 42, 32, 43, 42, 40, 41, 45, 42, 48, 45, 48, 44, 51, 41, 52, 51, 50, 51, 54
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OFFSET
| 1,5
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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.
We use the (nonstandard) terminology that the empty set (the proper divisors of 1) is not a subset of another set.
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FORMULA
| a(n)+A159070(n) = n. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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EXAMPLE
| a(8) = 2 counts k=6 with divisors set {1, 2, 3} (not subset of the divisors {1, 2, 4} of n = 8), and k=1 without proper divisors.
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CROSSREFS
| Cf.: A158974, A000040, A036234, A000720.
Sequence in context: A029139 A100927 A001687 * A116928 A034391 A206738
Adjacent sequences: A159069 A159070 A159071 * A159073 A159074 A159075
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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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