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A336422
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Number of ways to choose a divisor of a divisor of n, both having distinct prime exponents.
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13
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1, 3, 3, 6, 3, 5, 3, 10, 6, 5, 3, 13, 3, 5, 5, 15, 3, 13, 3, 13, 5, 5, 3, 24, 6, 5, 10, 13, 3, 7, 3, 21, 5, 5, 5, 21, 3, 5, 5, 24, 3, 7, 3, 13, 13, 5, 3, 38, 6, 13, 5, 13, 3, 24, 5, 24, 5, 5, 3, 20, 3, 5, 13, 28, 5, 7, 3, 13, 5, 7, 3, 42, 3, 5, 13, 13, 5, 7, 3
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OFFSET
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1,2
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COMMENTS
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A number has distinct prime exponents iff its prime signature is strict.
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LINKS
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EXAMPLE
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The a(n) ways for n = 1, 2, 4, 6, 8, 12, 30, 210:
1/1/1 2/1/1 4/1/1 6/1/1 8/1/1 12/1/1 30/1/1 210/1/1
2/2/1 4/2/1 6/2/1 8/2/1 12/2/1 30/2/1 210/2/1
2/2/2 4/2/2 6/2/2 8/2/2 12/2/2 30/2/2 210/2/2
4/4/1 6/3/1 8/4/1 12/3/1 30/3/1 210/3/1
4/4/2 6/3/3 8/4/2 12/3/3 30/3/3 210/3/3
4/4/4 8/4/4 12/4/1 30/5/1 210/5/1
8/8/1 12/4/2 30/5/5 210/5/5
8/8/2 12/4/4 210/7/1
8/8/4 12/12/1 210/7/7
8/8/8 12/12/2
12/12/3
12/12/4
12/12/12
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MATHEMATICA
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strdivs[n_]:=Select[Divisors[n], UnsameQ@@Last/@FactorInteger[#]&];
Table[Sum[Length[strdivs[d]], {d, strdivs[n]}], {n, 30}]
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CROSSREFS
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A336421 is the case of superprimorials.
A007425 counts divisors of divisors.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime exponents.
A327498 gives the maximum divisor with distinct prime exponents.
A336500 counts divisors with quotient also having distinct prime exponents.
A336568 = not a product of two numbers with distinct prime exponents.
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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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