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

0,2

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).

Links

Table of n, a(n) for n=0..7.

Example

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

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}]

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.

Sequence in context: A059040 A220895 A352308 * A189239 A074530 A159662

Adjacent sequences: A336418 A336419 A336420 * A336422 A336423 A336424

Keyword

nonn,more

Author

Gus Wiseman, Jul 25 2020

Status

approved