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A341677
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Number of strictly inferior prime-power divisors of n.
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14
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0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 3, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 3, 0, 2, 1, 2, 0, 2, 1, 3, 1, 1, 0, 4, 0, 1, 2, 2, 1, 2, 0, 2, 1, 3, 0, 4, 0, 1, 2, 2, 1, 2, 0, 4, 1, 1, 0, 4, 1, 1, 1
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OFFSET
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1,12
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COMMENTS
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We define a divisor d|n to be strictly inferior if d < n/d. Strictly inferior divisors are counted by A056924 and listed by A341674.
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LINKS
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EXAMPLE
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The strictly inferior prime-power divisors of n!:
n = 1 2 6 24 120 720 5040 40320
----------------------------------
. . 2 2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5
8 8 7 7
9 8 8
16 9 9
16 16
32
64
128
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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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The weakly inferior version is A333750.
The version for odd instead of prime-power divisors is A333805.
The version for prime instead of prime-power divisors is A333806.
The weakly superior version is A341593.
The version for squarefree instead of prime-power divisors is A341596.
The strictly superior version is A341644.
A001222 counts prime-power divisors.
A038548 counts superior (or inferior) divisors.
A056924 counts strictly superior (or strictly inferior) divisors.
- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A161908, A341591, A341592, A341676.
- Strictly Superior: A048098, A064052, A140271, A238535, A341594, A341595, A341642, A341643, A341645, A341646, A341673.
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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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