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A341592
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Number of squarefree superior divisors of n.
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25
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1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 1, 4, 1, 0, 2, 2, 2, 1, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 1, 2, 2, 1, 3, 1, 2, 1, 0, 2, 4, 1, 2, 2, 4, 1, 0, 1, 2, 1, 2, 2, 4, 1, 1, 0, 2, 1, 3, 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 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 strictly superior squarefree divisors (columns) of selected n:
1 6 8 30 60 210 420 630 1050 2310 4620 6930
------------------------------------------------------
1 3 . 6 10 15 21 30 35 55 70 105
6 10 15 21 30 35 42 66 77 110
15 30 30 35 42 70 70 105 154
30 35 42 70 105 77 110 165
42 70 105 210 105 154 210
70 105 210 110 165 231
105 210 154 210 330
210 165 231 385
210 330 462
231 385 770
330 462 1155
385 770 2310
462 1155
770 2310
1155
2310
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MAPLE
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with(numtheory):
a := n -> nops(select(d -> d*d >= n and issqrfree(d), divisors(n))):
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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 version for prime instead of squarefree divisors is A341591.
The version for prime powers instead of squarefree divisors is A341593.
The strictly superior case is A341595.
The version for odd instead of squarefree divisors is A341675.
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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STATUS
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approved
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