A336422 - OEIS

A336422

Number of ways to choose a divisor of a divisor of n, both having distinct prime exponents.

1, 3, 3, 6, 3, 5, 3, 10, 6, 5, 3, 13, 3, 5, 5, 15, 3, 13, 3, 13, 5, 5, 3, 24, 6, 5, 10, 13, 3, 7, 3, 21, 5, 5, 5, 21, 3, 5, 5, 24, 3, 7, 3, 13, 13, 5, 3, 38, 6, 13, 5, 13, 3, 24, 5, 24, 5, 5, 3, 20, 3, 5, 13, 28, 5, 7, 3, 13, 5, 7, 3, 42, 3, 5, 13, 13, 5, 7, 3

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OFFSET

1,2

COMMENTS

A number has distinct prime exponents iff its prime signature is strict.

LINKS

Table of n, a(n) for n=1..79.

EXAMPLE

The a(n) ways for n = 1, 2, 4, 6, 8, 12, 30, 210:

1/1/1 2/1/1 4/1/1 6/1/1 8/1/1 12/1/1 30/1/1 210/1/1

2/2/1 4/2/1 6/2/1 8/2/1 12/2/1 30/2/1 210/2/1

2/2/2 4/2/2 6/2/2 8/2/2 12/2/2 30/2/2 210/2/2

4/4/1 6/3/1 8/4/1 12/3/1 30/3/1 210/3/1

4/4/2 6/3/3 8/4/2 12/3/3 30/3/3 210/3/3

4/4/4 8/4/4 12/4/1 30/5/1 210/5/1

8/8/1 12/4/2 30/5/5 210/5/5

8/8/2 12/4/4 210/7/1

8/8/4 12/12/1 210/7/7

8/8/8 12/12/2

12/12/3

12/12/4

12/12/12

MATHEMATICA

strdivs[n_]:=Select[Divisors[n], UnsameQ@@Last/@FactorInteger[#]&];

Table[Sum[Length[strdivs[d]], {d, strdivs[n]}], {n, 30}]

CROSSREFS

A336421 is the case of superprimorials.

A007425 counts divisors of divisors.

A130091 lists numbers with distinct prime exponents.

A181796 counts divisors with distinct prime exponents.

A327498 gives the maximum divisor with distinct prime exponents.

A336500 counts divisors with quotient also having distinct prime exponents.

A336568 = not a product of two numbers with distinct prime exponents.

Cf. A000005, A001055, A005117, A032741, A071625, A118914, A124010, A336419, A336420.

Sequence in context: A184849 A335870 A339496 * A040007 A351024 A110634

Adjacent sequences: A336419 A336420 A336421 * A336423 A336424 A336425

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 26 2020

STATUS

approved