OFFSET

1,2

COMMENTS

A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.

EXAMPLE

The a(1) = 1 through a(16) = 5 divisors:

1 1 1 1 1 2 1 1 1 2 1 1 1 2 3 1

2 3 2 5 3 7 2 3 5 11 3 13 7 5 2

4 4 9 4 4

8 12 8

16

MATHEMATICA

Table[Length[Select[Divisors[n], UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[n/#]&]], {n, 25}]

CROSSREFS

A336419 is the version for superprimorials.

A336568 gives positions of zeros.

A336869 is the restriction to factorials.

A007425 counts divisors of divisors.

A056924 counts divisors greater than their quotient.

A074206 counts chains of divisors from n to 1.

A130091 lists numbers with distinct prime exponents.

A181796 counts divisors with distinct prime multiplicities.

A327498 gives the maximum divisor with distinct prime multiplicities.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 06 2020

STATUS

approved