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A337071
Number of strict chains of divisors starting with n!.
12
1, 1, 2, 6, 40, 264, 3776, 40256, 1168000, 34204032, 1107791872, 23233380352, 1486675898368, 38934372315136, 1999103691427840, 132874800979423232, 20506322412604129280, 776179999255323115520, 107455579038104865996800, 4651534843901106606571520, 731092060557632280262082560
OFFSET
0,3
FORMULA
a(n) = 2*A337105(n) for n > 1.
a(n) = A067824(n!).
EXAMPLE
The a(1) = 1 through a(3) = 6 chains:
1 2 6
2/1 6/1
6/2
6/3
6/2/1
6/3/1
The a(4) = 40 chains:
24 24/1 24/2/1 24/4/2/1 24/8/4/2/1
24/2 24/3/1 24/6/2/1 24/12/4/2/1
24/3 24/4/1 24/6/3/1 24/12/6/2/1
24/4 24/4/2 24/8/2/1 24/12/6/3/1
24/6 24/6/1 24/8/4/1
24/8 24/6/2 24/8/4/2
24/12 24/6/3 24/12/2/1
24/8/1 24/12/3/1
24/8/2 24/12/4/1
24/8/4 24/12/4/2
24/12/1 24/12/6/1
24/12/2 24/12/6/2
24/12/3 24/12/6/3
24/12/4
24/12/6
MATHEMATICA
chnsc[n_]:=Prepend[Join@@Table[Prepend[#, n]&/@chnsc[d], {d, Most[Divisors[n]]}], {n}];
Table[Length[chnsc[n!]], {n, 0, 5}]
CROSSREFS
A325617 is the maximal case.
A337070 is the version for superprimorials.
A337074 counts the case with distinct prime multiplicities.
A337105 is the case ending with one.
A000005 counts divisors.
A000142 lists factorial numbers.
A027423 counts divisors of factorial numbers.
A067824 counts chains of divisors starting with n.
A074206 counts chains of divisors from n to 1.
A076716 counts factorizations of factorial numbers.
A253249 counts chains of divisors.
Sequence in context: A119692 A264152 A333631 * A354313 A351739 A098854
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 16 2020
EXTENSIONS
a(19)-a(20) from Alois P. Heinz, Aug 23 2020
STATUS
approved