%I #12 Aug 31 2020 19:49:50
%S 1,2,4,10,24,64,184,536,1608,5104,16448,55136,187136,658624,2339648,
%T 8618208,31884640,121733120,468209408,1849540416,7342849216
%N 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.
%C A number has distinct prime exponents iff its prime signature is strict.
%C The n-th superprimorial or Chernoff number is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
%e The a(0) = 1 through a(3) = 10 divisors:
%e 1 2 12 360
%e -----------------
%e 1 1 1 1
%e 2 3 5
%e 4 8
%e 12 9
%e 18
%e 20
%e 40
%e 45
%e 72
%e 360
%t chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t Table[Length[Select[Divisors[chern[n]],UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&]],{n,0,6}]
%o (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))))))}
%o a(n)={recurse(n,1,1,1)} \\ _Andrew Howroyd_, Aug 30 2020
%Y A000110 shifted once to the left dominates this sequence.
%Y A006939 lists superprimorials or Chernoff numbers.
%Y A022915 counts permutations of prime indices of superprimorials.
%Y A130091 lists numbers with distinct prime exponents.
%Y A181796 counts divisors with distinct prime exponents.
%Y A181818 gives products of superprimorials.
%Y A317829 counts factorizations of superprimorials.
%Y A336417 counts perfect-power divisors of superprimorials.
%Y Cf. A000005, A000178, A008278, A071625, A076954, A118914, A124010, A327498, A327527, A336420, A336421, A336426, A336500, A336568.
%K nonn,more
%O 0,2
%A _Gus Wiseman_, Jul 25 2020
%E a(10)-a(20) from _Andrew Howroyd_, Aug 31 2020