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A341642
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Number of strictly superior prime divisors of n.
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26
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0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1
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OFFSET
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1
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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.
All terms are binary numbers.
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LINKS
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EXAMPLE
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The sequence of sets of strictly superior prime divisors of each positive integer begins: {}, {2}, {3}, {}, {5}, {3}, {7}, {}, {}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {5}, ...
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MATHEMATICA
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Table[Length[Select[Divisors[n], PrimeQ[#]&&#>n/#&]], {n, 100}]
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CROSSREFS
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The strictly inferior version is A333806.
Dominated by A341591 (the weak version).
The version for odd instead of prime divisors is A341594.
The version for squarefree instead of prime divisors is A341595.
The strictly superior prime divisors themselves are listed by A341643.
The version for prime-power instead of prime divisors is A341644.
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, A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341592, A341593, 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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