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A336500
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Number of divisors d|n with distinct prime multiplicities such that the quotient n/d also has distinct prime multiplicities.
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24
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1, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 4, 2, 2, 2, 5, 2, 4, 2, 4, 2, 2, 2, 6, 3, 2, 4, 4, 2, 0, 2, 6, 2, 2, 2, 6, 2, 2, 2, 6, 2, 0, 2, 4, 4, 2, 2, 8, 3, 4, 2, 4, 2, 6, 2, 6, 2, 2, 2, 4, 2, 2, 4, 7, 2, 0, 2, 4, 2, 0, 2, 8, 2, 2, 4, 4, 2, 0, 2, 8, 5, 2, 2, 4, 2, 2, 2
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OFFSET
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1,2
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COMMENTS
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A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(16) = 5 divisors:
1 1 1 1 1 2 1 1 1 2 1 1 1 2 3 1
2 3 2 5 3 7 2 3 5 11 3 13 7 5 2
4 4 9 4 4
8 12 8
16
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MATHEMATICA
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Table[Length[Select[Divisors[n], UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[n/#]&]], {n, 25}]
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CROSSREFS
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A336419 is the version for superprimorials.
A336869 is the restriction to factorials.
A007425 counts divisors of divisors.
A056924 counts divisors greater than their quotient.
A074206 counts chains of divisors from n to 1.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime multiplicities.
A327498 gives the maximum divisor with distinct prime multiplicities.
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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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