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%I #7 Aug 06 2020 23:28:49
%S 1,1,3,5,24,38,132,195,570,1588,4193,6086,14561,19232,37142,106479,
%T 207291,266871,549726,674330,1465399
%N Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.
%e The a(4) = 24 divisors of divisors:
%e 1/1 2/1 3/1 4/1 8/1 12/1 24/1
%e 2/2 3/3 4/2 8/2 12/2 24/2
%e 4/4 8/4 12/3 24/3
%e 8/8 12/4 24/4
%e 12/12 24/8
%e 24/12
%e 24/24
%t strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n];
%t Table[Total[Cases[Divisors[n!],d_?strsigQ:>Count[Divisors[d],e_?strsigQ]]],{n,0,20}]
%Y A336422 is the non-factorial generalization.
%Y A130091 lists numbers with distinct prime exponents.
%Y A181796 counts divisors with distinct prime exponents.
%Y A327526 gives the maximum divisor of n with equal prime exponents.
%Y A327498 gives the maximum divisor of n with distinct prime exponents.
%Y A336414 counts divisors of n! with distinct prime exponents.
%Y A336415 counts divisors of n! with equal prime exponents.
%Y A336423 counts chains in A130091, with maximal version A336569.
%Y Cf. A000005, A000110, A098859, A118914, A124010, A336424, A336500, A336568, A336570, A336571, A336865, A336866, A336869.
%Y Factorial numbers: A000142, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327499, A336416, A336418, A336617.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Aug 06 2020
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