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A336425
Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.
6
1, 1, 3, 5, 24, 38, 132, 195, 570, 1588, 4193, 6086, 14561, 19232, 37142, 106479, 207291, 266871, 549726, 674330, 1465399, 3086598, 5939574, 7182133, 12324512, 28968994, 46819193, 82873443, 165205159, 196666406, 350397910, 406894074, 593725529, 1229814478, 1853300600, 4024414209, 6049714096, 6968090487, 9700557121, 16810076542, 26339337285
OFFSET
0,3
LINKS
EXAMPLE
The a(4) = 24 divisors of divisors:
1/1 2/1 3/1 4/1 8/1 12/1 24/1
2/2 3/3 4/2 8/2 12/2 24/2
4/4 8/4 12/3 24/3
8/8 12/4 24/4
12/12 24/8
24/12
24/24
MATHEMATICA
strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n];
Table[Total[Cases[Divisors[n!], d_?strsigQ:>Count[Divisors[d], e_?strsigQ]]], {n, 0, 20}]
CROSSREFS
A336422 is the non-factorial generalization.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime exponents.
A327526 gives the maximum divisor of n with equal prime exponents.
A327498 gives the maximum divisor of n with distinct prime exponents.
A336414 counts divisors of n! with distinct prime exponents.
A336415 counts divisors of n! with equal prime exponents.
A336423 counts chains in A130091, with maximal version A336569.
Sequence in context: A005761 A200948 A275148 * A230985 A286427 A290509
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 06 2020
EXTENSIONS
Terms a(21) onward from Max Alekseyev, Nov 07 2024
STATUS
approved