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%I #13 Nov 20 2020 17:15:57
%S 1,1,2,0,28,0,768,0,0,0,42155360,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities), starting with n!.
%C Support appears to be {0, 1, 2, 4, 6, 10}.
%F a(n) = 2*A337104(n) = 2*A336423(n!) for n > 1.
%e The a(4) = 28 chains:
%e 24 24/1 24/2/1 24/4/2/1 24/8/4/2/1
%e 24/2 24/3/1 24/8/2/1 24/12/4/2/1
%e 24/3 24/4/1 24/8/4/1
%e 24/4 24/4/2 24/8/4/2
%e 24/8 24/8/1 24/12/2/1
%e 24/12 24/8/2 24/12/3/1
%e 24/8/4 24/12/4/1
%e 24/12/1 24/12/4/2
%e 24/12/2
%e 24/12/3
%e 24/12/4
%t chnsc[n_]:=If[!UnsameQ@@Last/@FactorInteger[n],{},If[n==1,{{1}},Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,Most[Divisors[n]]}],{n}]]];
%t Table[Length[chnsc[n!]],{n,0,6}]
%Y A336867 is the complement of the support.
%Y A336868 is the characteristic function (image under A057427).
%Y A336942 is half the version for superprimorials (n > 1).
%Y A337071 does not require distinct prime multiplicities.
%Y A337104 is the case of chains ending with 1.
%Y A000005 counts divisors.
%Y A000142 lists factorial numbers.
%Y A027423 counts divisors of factorial numbers.
%Y A067824 counts chains of divisors starting with n.
%Y A074206 counts chains of divisors from n to 1.
%Y A076716 counts factorizations of factorial numbers.
%Y A130091 lists numbers with distinct prime multiplicities.
%Y A181796 counts divisors with distinct prime multiplicities.
%Y A253249 counts chains of divisors.
%Y A327498 gives the maximum divisor with distinct prime multiplicities.
%Y A336414 counts divisors of n! with distinct prime multiplicities.
%Y A336415 counts divisors of n! with equal prime multiplicities.
%Y A336423 counts chains using A130091, with maximal case A336569.
%Y A336571 counts chains of divisors 1 < d < n using A130091.
%Y Cf. A000110, A001055, A002033, A007489, A022559, A048656, A071626, A098859, A124010, A167865, A325617, A336416, A336424.
%K nonn
%O 0,3
%A _Gus Wiseman_, Aug 16 2020
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