OFFSET
1,2
COMMENTS
A number has distinct prime exponents iff its prime signature is strict.
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2020
STATUS
approved