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A241556
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Number of prime anti-divisors m of n.
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2
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0, 0, 1, 1, 2, 0, 3, 2, 1, 2, 3, 1, 3, 1, 1, 2, 5, 2, 3, 2, 1, 2, 3, 1, 4, 2, 3, 4, 3, 0, 3, 4, 3, 2, 3, 0, 3, 4, 3, 1, 2, 2, 5, 2, 3, 4, 5, 2, 3, 2, 1, 3, 4, 0, 3, 2, 3, 4, 5, 3, 4, 3, 2, 2, 3, 2, 5, 2, 1, 2, 5, 4, 5, 2, 1, 2, 5, 2, 3, 4, 3, 3, 4, 1, 4, 2, 3, 4, 3, 0, 3, 4, 5, 4, 3, 0
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OFFSET
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1,5
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COMMENTS
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The maximum value of a(n) is 9 for 1 <= n <= 10000.
There are 167 instances of a(n) = 0 for 1 <= n <= 10000 (See A241557).
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LINKS
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EXAMPLE
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a(10) = 2, since 10 has 3 anti-divisors {3, 4, 7}; only {3, 7} are prime.
a(9223) = 9; these are {2, 3, 5, 7, 11, 13, 17, 31, 43}.
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MATHEMATICA
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primeAntiDivisors[n_] := Select[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)], PrimeQ]; a241556[n_Integer] := Map[Length[primeAntiDivisors[#]] &, Range[n]]; a241556[120]
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CROSSREFS
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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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