OFFSET
1,2
COMMENTS
This sequence has similarities with A209260; here we consider quotients of factorial numbers, there differences of triangular numbers.
The n-th row is included in the n-th row of A068424 and has greatest term n!.
As a flat sequence, we have a permutation of the positive integers (any n > 0 appears among the first n rows, see A348401).
For any prime number p, the p-th row contains p-1 terms.
LINKS
EXAMPLE
Triangle begins:
1;
2;
3, 6;
4, 12, 24;
5, 20, 60, 120;
30, 360, 720;
7, 42, 210, 840, 2520, 5040;
8, 56, 336, 1680, 6720, 20160, 40320;
9, 72, 504, 3024, 15120, 60480, 181440, 362880;
10, 90, 30240, 151200, 604800, 1814400, 3628800;
11, 110, 990, 7920, 55440, 332640, 1663200, 6652800, 19958400, 39916800;
...
PROG
(PARI) s=[]; for (n=1, 11, p=1; forstep (m=n, 1, -1, if (!setsearch(s, p*=m), s=setunion(s, [p]); print1 (p", "))))
(Python)
from math import factorial
def auptor(rows):
alst, aset = [1], {1}
for n in range(2, rows+1):
fn = factorial(n)
for m in range(n-1, 0, -1):
fm = factorial(m)
q, r = divmod(fn, factorial(m))
if r == 0 and q not in aset:
alst.append(q); aset.add(q)
return alst
print(auptor(11)) # Michael S. Branicky, Oct 17 2021
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Oct 16 2021
STATUS
approved