|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
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
|
A337070 is the version for superprimorials.
A337074 counts the case with distinct prime multiplicities.
A337105 is the case ending with one.
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|