|
| |
|
|
A337107
|
|
Irregular triangle read by rows where T(n,k) is the number of strict length-k chains of divisors from n! to 1.
|
|
8
|
|
|
|
1, 0, 1, 0, 1, 2, 0, 1, 6, 9, 4, 0, 1, 14, 45, 52, 20, 0, 1, 28, 183, 496, 655, 420, 105, 0, 1, 58, 633, 2716, 5755, 6450, 3675, 840, 0, 1, 94, 1659, 11996, 46235, 106806, 155869, 145384, 84276, 27720, 3960
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
Row n > 1 appears to be row n! of A334996.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Triangle begins:
1
0 1
0 1 2
0 1 6 9 4
0 1 14 45 52 20
0 1 28 183 496 655 420 105
0 1 58 633 2716 5755 6450 3675 840
Row n = 4 counts the following chains:
24/1 24/2/1 24/4/2/1 24/8/4/2/1
24/3/1 24/6/2/1 24/12/4/2/1
24/4/1 24/6/3/1 24/12/6/2/1
24/6/1 24/8/2/1 24/12/6/3/1
24/8/1 24/8/4/1
24/12/1 24/12/2/1
24/12/3/1
24/12/4/1
24/12/6/1
|
|
|
MAPLE
|
b:= proc(n) option remember; expand(x*(`if`(n=1, 1, 0) +
add(b(d), d=numtheory[divisors](n) minus {n})))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n!)):
|
|
|
MATHEMATICA
|
nv=5;
chnsc[n_]:=Select[Prepend[Join@@Table[Prepend[#, n]&/@chnsc[d], {d, DeleteCases[Divisors[n], n]}], {n}], MemberQ[#, 1]&];
Table[Length[Select[chnsc[n!], Length[#]==k&]], {n, nv}, {k, 1+PrimeOmega[n!]}]
|
|
|
CROSSREFS
|
A097805 is the restriction to powers of 2.
A074206 counts chains of divisors from n to 1.
A027423 counts divisors of factorial numbers.
A067824 counts chains of divisors starting with n.
A076716 counts factorizations of factorial numbers.
A337071 counts chains starting with n!.
|
|
|
KEYWORD
|
nonn,tabf
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
