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A341675
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Number of superior odd divisors of n.
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27
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1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 2, 0, 1, 2, 1, 1, 3, 1, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1, 3, 0, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 0, 3, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 1, 1, 3, 1, 1, 2, 1, 1, 4
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OFFSET
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1,9
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COMMENTS
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We define a divisor d|n to be superior if d >= n/d. Superior divisors are counted by A038548 and listed by A161908.
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LINKS
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EXAMPLE
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The superior odd divisors of selected n:
n = 1 9 45 105 225 315 945 1575 1890 2835 3465 8190
-----------------------------------------------------------
1 9 45 105 225 315 945 1575 945 2835 3465 4095
3 15 35 75 105 315 525 315 945 1155 1365
9 21 45 63 189 315 189 567 693 819
15 25 45 135 225 135 405 495 585
15 35 105 175 105 315 385 455
21 63 105 63 189 315 315
45 75 45 135 231 273
35 63 105 165 195
45 81 105 117
63 99 105
77 91
63
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MATHEMATICA
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Table[Length[Select[Divisors[n], OddQ[#]&&#>=n/#&]], {n, 100}]
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PROG
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CROSSREFS
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Positions of 0's (except a(1)) are A116882.
The version for prime instead of odd divisors is A341591.
The version for squarefree instead of odd divisors is A341592.
The version for prime-power instead of odd divisors is A341593.
The strictly superior case is A341594.
A033676 selects the greatest inferior divisor.
A033677 selects the smallest superior divisor.
A038548 counts superior (or inferior) divisors.
A056924 counts strictly superior (or strictly inferior) divisors.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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