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A341644
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Number of strictly superior prime-power divisors of n.
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23
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0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1
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OFFSET
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1,8
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COMMENTS
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We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.
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LINKS
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EXAMPLE
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The strictly superior prime power divisors of random selected n:
n = 768 2048 5103 6144 8192 8722 9433 9984
----------------------------------------------
32 64 81 128 128 9433 128
64 128 243 256 256 256
128 256 729 512 512
256 512 1024 1024
1024 2048 2048
2048 4096
8192
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MATHEMATICA
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Table[Length[Select[Divisors[n], PrimePowerQ[#]&&#>n/#&]], {n, 100}]
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CROSSREFS
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Positions of zeros (after the first) are A051283.
Dominated by A341593 (the weakly superior version).
The version for odd instead of prime divisors is A341594.
The version for squarefree instead of prime divisors is A341595.
The version for prime instead of prime-power divisors is A341642.
The strictly inferior version is A341677.
A001222 counts prime-power divisors.
A140271 selects the smallest strictly superior divisor.
A038548 counts superior (or inferior) divisors.
A056924 counts strictly superior (or strictly inferior) divisors.
A341673 lists strictly superior divisors.
- Superior: A033677, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341591, A341592, A341675, A341676.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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