cp's OEIS Frontend

A337071 Number of strict chains of divisors starting with n!.

%I A337071 #14 Sep 02 2020 23:07:06
%S A337071 1,1,2,6,40,264,3776,40256,1168000,34204032,1107791872,23233380352,
%T A337071 1486675898368,38934372315136,1999103691427840,132874800979423232,
%U A337071 20506322412604129280,776179999255323115520,107455579038104865996800,4651534843901106606571520,731092060557632280262082560
%N A337071 Number of strict chains of divisors starting with n!.
%F A337071 a(n) = 2*A337105(n) for n > 1.
%F A337071 a(n) = A067824(n!).
%e A337071 The a(1) = 1 through a(3) = 6 chains:
%e A337071   1  2    6
%e A337071      2/1  6/1
%e A337071           6/2
%e A337071           6/3
%e A337071           6/2/1
%e A337071           6/3/1
%e A337071 The a(4) = 40 chains:
%e A337071   24  24/1   24/2/1   24/4/2/1   24/8/4/2/1
%e A337071       24/2   24/3/1   24/6/2/1   24/12/4/2/1
%e A337071       24/3   24/4/1   24/6/3/1   24/12/6/2/1
%e A337071       24/4   24/4/2   24/8/2/1   24/12/6/3/1
%e A337071       24/6   24/6/1   24/8/4/1
%e A337071       24/8   24/6/2   24/8/4/2
%e A337071       24/12  24/6/3   24/12/2/1
%e A337071              24/8/1   24/12/3/1
%e A337071              24/8/2   24/12/4/1
%e A337071              24/8/4   24/12/4/2
%e A337071              24/12/1  24/12/6/1
%e A337071              24/12/2  24/12/6/2
%e A337071              24/12/3  24/12/6/3
%e A337071              24/12/4
%e A337071              24/12/6
%t A337071 chnsc[n_]:=Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,Most[Divisors[n]]}],{n}];
%t A337071 Table[Length[chnsc[n!]],{n,0,5}]
%Y A337071 A325617 is the maximal case.
%Y A337071 A337070 is the version for superprimorials.
%Y A337071 A337074 counts the case with distinct prime multiplicities.
%Y A337071 A337105 is the case ending with one.
%Y A337071 A000005 counts divisors.
%Y A337071 A000142 lists factorial numbers.
%Y A337071 A027423 counts divisors of factorial numbers.
%Y A337071 A067824 counts chains of divisors starting with n.
%Y A337071 A074206 counts chains of divisors from n to 1.
%Y A337071 A076716 counts factorizations of factorial numbers.
%Y A337071 A253249 counts chains of divisors.
%Y A337071 Cf. A001013, A001055, A002033, A022559, A124010, A167865, A336941, A336942.
%K A337071 nonn
%O A337071 0,3
%A A337071 _Gus Wiseman_, Aug 16 2020
%E A337071 a(19)-a(20) from _Alois P. Heinz_, Aug 23 2020