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%I #14 Aug 30 2020 20:23:55
%S 1,1,1,3,20,132,1888,20128,584000,17102016,553895936,11616690176,
%T 743337949184,19467186157568,999551845713920,66437400489711616,
%U 10253161206302064640,388089999627661557760,53727789519052432998400,2325767421950553303285760,365546030278816140131041280
%N Number of strict chains of divisors from n! to 1.
%H Andrew Howroyd, <a href="/A337105/b337105.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = A337071(n)/2 for n > 1.
%F a(n) = A074206(n!).
%e The a(4) = 20 chains:
%e 24/1 24/2/1 24/4/2/1 24/8/4/2/1
%e 24/3/1 24/6/2/1 24/12/4/2/1
%e 24/4/1 24/6/3/1 24/12/6/2/1
%e 24/6/1 24/8/2/1 24/12/6/3/1
%e 24/8/1 24/8/4/1
%e 24/12/1 24/12/2/1
%e 24/12/3/1
%e 24/12/4/1
%e 24/12/6/1
%p b:= proc(n) option remember; 1 +
%p add(b(d), d=numtheory[divisors](n) minus {n})
%p end:
%p a:= n-> ceil(b(n!)/2):
%p seq(a(n), n=0..14); # _Alois P. Heinz_, Aug 23 2020
%t chnsc[n_]:=Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,DeleteCases[Divisors[n],1|n]}],{n}];
%t Table[Length[chnsc[n!]],{n,0,5}]
%Y A325617 is the maximal case.
%Y A336941 is the version for superprimorials.
%Y A337104 counts the case with distinct prime multiplicities.
%Y A337071 is the case not necessarily ending with 1.
%Y A000005 counts divisors.
%Y A000142 lists factorial numbers.
%Y A001055 counts factorizations.
%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 A253249 counts chains of divisors.
%Y A336423 counts chains using A130091, with maximal case A336569.
%Y A336942 counts chains using A130091 from A006939(n) to 1.
%Y Cf. A001013, A001055, A022559, A124010, A167865, A337070, A337074.
%K nonn
%O 0,4
%A _Gus Wiseman_, Aug 17 2020
%E a(19)-a(20) from _Alois P. Heinz_, Aug 22 2020
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