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A336419
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Number of divisors d of the n-th superprimorial A006939(n) with distinct prime exponents such that the quotient A006939(n)/d also has distinct prime exponents.
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15
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1, 2, 4, 10, 24, 64, 184, 536, 1608, 5104, 16448, 55136, 187136, 658624, 2339648, 8618208, 31884640, 121733120, 468209408, 1849540416, 7342849216
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OFFSET
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0,2
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COMMENTS
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A number has distinct prime exponents iff its prime signature is strict.
The n-th superprimorial or Chernoff number is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
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LINKS
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EXAMPLE
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The a(0) = 1 through a(3) = 10 divisors:
1 2 12 360
-----------------
1 1 1 1
2 3 5
4 8
12 9
18
20
40
45
72
360
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MATHEMATICA
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chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
Table[Length[Select[Divisors[chern[n]], UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&]], {n, 0, 6}]
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PROG
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(PARI) recurse(n, k, b, d)={if(k>n, 1, sum(i=0, k, if((i==0||!bittest(b, i)) && (i==k||!bittest(d, k-i)), self()(n, k+1, bitor(b, 1<<i), bitor(d, 1<<(k-i))))))}
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CROSSREFS
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A000110 shifted once to the left dominates this sequence.
A006939 lists superprimorials or Chernoff numbers.
A022915 counts permutations of prime indices of superprimorials.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime exponents.
A181818 gives products of superprimorials.
A317829 counts factorizations of superprimorials.
A336417 counts perfect-power divisors of superprimorials.
Cf. A000005, A000178, A008278, A071625, A076954, A118914, A124010, A327498, A327527, A336420, A336421, A336426, A336500, A336568.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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