OFFSET
0,2
COMMENTS
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).
EXAMPLE
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
MATHEMATICA
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}]
PROG
(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))))))}
a(n)={recurse(n, 1, 1, 1)} \\ Andrew Howroyd, Aug 30 2020
CROSSREFS
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.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 25 2020
EXTENSIONS
a(10)-a(20) from Andrew Howroyd, Aug 31 2020
STATUS
approved