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A341596
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Number of strictly inferior squarefree divisors of n.
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28
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0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 4, 1, 2, 3, 2, 1, 4, 1, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 5, 1, 2, 3, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 2, 3, 2, 2, 4, 1, 3, 2, 2, 1, 5, 2, 2, 2
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OFFSET
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1,6
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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 squarefree divisors of selected n:
n = 1 2 6 12 30 60 120 210 240 420 630 1050 1260
--------------------------------------------------------
{} 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3
5 5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6
10 7 10 7 7 7 7
10 15 10 10 10 10
14 14 14 14 14
15 15 15 15
21 21 21
30 30
35
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MATHEMATICA
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Table[Length[Select[Divisors[n], SquareFreeQ[#]&&#<n/#&]], {n, 100}]
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CROSSREFS
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The weakly inferior version is A333749.
The version counting odd instead of squarefree divisors is A333805.
The version counting prime instead of squarefree divisors is A333806.
The weakly superior version is A341592.
The strictly superior version is A341595.
The version counting prime-power instead of squarefree divisors is A341677.
A001222 counts prime power divisors.
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.
- Superior: A051283, A059172, A063538, A063539, A070038, A116882, A116883, A161908, A341591, A341593, A341675, A341676.
- Strictly Superior: A048098, A064052, A140271, A238535, A341594, A341642, A341643, A341644, 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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