A336421 Number of ways to choose a divisor of a divisor, both having distinct prime exponents, of the n-th superprimorial number A006939(n).

1, 3, 13, 76, 571, 5309, 59341, 780149

Offset: 0

Author

Gus Wiseman, Jul 25 2020

Keywords

• nonn
• more

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).

Examples

			The a(2) = 13 ways:
  12/1/1  12/2/1  12/3/1  12/4/1  12/12/1
          12/2/2  12/3/3  12/4/2  12/12/2
                          12/4/4  12/12/3
                                  12/12/4
                                  12/12/12
		

Crossrefs

A000258 shifted once to the left is dominated by this sequence.

A336422 is the generalization to non-superprimorials.

A000110 counts divisors of superprimorials with distinct prime exponents.

A006939 lists superprimorials or Chernoff numbers.

A008302 counts divisors of superprimorials by bigomega.

A022915 counts permutations of prime indices of superprimorials.

A076954 can be used instead of A006939.

A130091 lists numbers with distinct prime exponents.

A181796 counts divisors with distinct prime exponents.

A181818 gives products of superprimorials.

A317829 counts factorizations of superprimorials.

Cf. A000005, A008278, A027423, A071625, A118914, A124010, A327498, A336417, A336419, A336420, A336426, A336500, A336568.

Programs

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
strsig[n_]:=UnsameQ@@Last/@FactorInteger[n];
Table[Total[Cases[Divisors[chern[n]],d_?strsig:>Count[Divisors[d],e_?strsig]]],{n,0,5}]