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A336422
Number of ways to choose a divisor of a divisor of n, both having distinct prime exponents.
13
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
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.
Sequence in context: A184849 A335870 A339496 * A040007 A351024 A110634
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2020
STATUS
approved