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A336425
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Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.
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5
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1, 1, 3, 5, 24, 38, 132, 195, 570, 1588, 4193, 6086, 14561, 19232, 37142, 106479, 207291, 266871, 549726, 674330, 1465399
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(4) = 24 divisors of divisors:
1/1 2/1 3/1 4/1 8/1 12/1 24/1
2/2 3/3 4/2 8/2 12/2 24/2
4/4 8/4 12/3 24/3
8/8 12/4 24/4
12/12 24/8
24/12
24/24
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MATHEMATICA
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strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n];
Table[Total[Cases[Divisors[n!], d_?strsigQ:>Count[Divisors[d], e_?strsigQ]]], {n, 0, 20}]
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CROSSREFS
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A336422 is the non-factorial generalization.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime exponents.
A327526 gives the maximum divisor of n with equal prime exponents.
A327498 gives the maximum divisor of n with distinct prime exponents.
A336414 counts divisors of n! with distinct prime exponents.
A336415 counts divisors of n! with equal prime exponents.
Cf. A000005, A000110, A098859, A118914, A124010, A336424, A336500, A336568, A336570, A336571, A336865, A336866, A336869.
Factorial numbers: A000142, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327499, A336416, A336418, A336617.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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