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Search: id:A159073
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| A159073 |
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Sum of the 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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+0
3
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| 0, 2, 5, 9, 10, 20, 17, 29, 26, 31, 28, 67, 41, 59, 65, 69, 58, 95, 77, 119, 107, 103, 100, 179, 125, 130, 136, 154, 129, 228, 160, 220, 202, 198, 220, 280, 197, 239, 245, 320, 238, 334, 281, 359, 402, 331, 328, 487, 377, 417, 388, 418, 381, 499, 461, 556, 447, 443, 440
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Here proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as defined in A032741.
Terms of the sum are counted in A159070.
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FORMULA
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a(n) = A158975(n) - 1.
If p = prime, element of A000040, a(p) = A158662(p) - 1 = A014284(A036234(p)) - 1.
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EXAMPLE
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a(8) = 29 is the sum of the following six 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} of n = 8. 2 + 3 + 4 + 5 + 7 + 8 = 29.
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CROSSREFS
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Cf.: A158975, A000040, A014284, A036234.
Sequence in context: A047619 A046711 A095347 this_sequence A088343 A110781 A115248
Adjacent sequences: A159070 A159071 A159072 this_sequence A159074 A159075 A159076
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Apr 04 2009
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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