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

Author

Gus Wiseman, Aug 06 2020

Keywords

• nonn
• more

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.

Examples

			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
		

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.

Programs

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}]