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Search: id:A066241
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| A066241 |
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1 + number of anti-divisors of n. |
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+0
6
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| 1, 1, 2, 2, 3, 2, 4, 3, 3, 4, 4, 3, 5, 4, 4, 3, 6, 5, 4, 4, 4, 6, 6, 3, 6, 4, 6, 6, 4, 4, 6, 7, 6, 4, 6, 3, 6, 8, 6, 5, 5, 6, 6, 4, 8, 6, 6, 4, 7, 7, 4, 8, 8, 4, 6, 4, 6, 8, 8, 7, 5, 6, 8, 3, 6, 6, 10, 8, 4, 6, 6, 7, 8, 6, 6, 6, 10, 6, 4, 6, 7, 8, 8, 5, 9, 6, 8, 8, 4, 6, 6, 6, 8, 10, 10, 2, 8, 9, 6, 5
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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See A066272 for definition of anti-divisor.
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LINKS
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Jon Perry, Anti-divisors
Jon Perry, The Anti-divisor [Cached copy]
Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]
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EXAMPLE
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For example, n = 18: 2n-1, 2n, 2n+1 are 35, 36, 37 with odd divisors > 1 {3,7,35}, {3,9}, {37} and quotients 7, 5, 1, 12, 4, 1, so the anti-divisors of 12 are 4, 5, 7, 12. Therefore a(18) = 1 + 4 = 5.
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MATHEMATICA
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antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 &], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 &], 2n/Select[ Divisors[2*n], OddQ[ # ] && # != 1 &]]], # < n &]; Table[ Length[ antid[n]] + 1, {n, 1, 100} ]
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CROSSREFS
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Cf. A058838. Equals 1 + A066272(n).
Sequence in context: A086375 A107324 A023522 this_sequence A060025 A067399 A106737
Adjacent sequences: A066238 A066239 A066240 this_sequence A066242 A066243 A066244
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 31, 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 03 2002
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