A336871 Number of divisors d of A076954(n) with distinct prime multiplicities such that the numerator of A006939(n)/d also has distinct prime multiplicities.

1, 2, 4, 11, 28, 96, 309, 1256, 4676, 21647

Offset

0,2

Comments

The sequence A006939 is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).

The sequence A076954 is A076954(n) = Product_{i=1..n} prime(i)^i.

Links

Table of n, a(n) for n=0..9.

Example

The a(0) = 1 through a(3) = 11 divisors:
  1  2  18   2250
     1   9   1125
         3    375
         1    125
               75
               45
               25
               18
                9
                5
                1

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
cochern[n_]:=Product[Prime[i]^i, {i, n}];
Table[Length[Select[Divisors[cochern[n]], UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&]], {n, 0, 5}]

Crossrefs

A336419 is the version for superprimorials.

A336500 is the generalization to all positive integers.

A000005 counts divisors.

A006939 lists superprimorials or Chernoff numbers.

A007425 counts divisors of divisors.

A076954 is a sister of superprimorials.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

A327523 counts factorizations of elements of A130091 using elements of A130091.

A336422 counts divisible pairs of divisors, both in A130091.

A336424 counts factorizations using A130091.

Cf. A001055, A022559, A022915, A027423, A091050, A124010, A317829, A327498, A327527, A336420, A336421, A336571.

Sequence in context: A148138 A005503 A148139 * A061860 A093960 A267912

Adjacent sequences: A336868 A336869 A336870 * A336872 A336873 A336874

Keyword

nonn,more

Author

Gus Wiseman, Aug 06 2020

Status

approved