OFFSET
1,7
LINKS
Alois P. Heinz, Rows n = 1..5000, flattened
EXAMPLE
Sequence of rows begins:
1: {1} 16: {1,4,6,4,1}
2: {1,1} 17: {1,1}
3: {1,1} 18: {1,5,7,3}
4: {1,2,1} 19: {1,1}
5: {1,1} 20: {1,5,7,3}
6: {1,3,2} 21: {1,3,2}
7: {1,1} 22: {1,3,2}
8: {1,3,3,1} 23: {1,1}
9: {1,2,1} 24: {1,7,15,13,4}
10: {1,3,2} 25: {1,2,1}
11: {1,1} 26: {1,3,2}
12: {1,5,7,3} 27: {1,3,3,1}
13: {1,1} 28: {1,5,7,3}
14: {1,3,2} 29: {1,1}
15: {1,3,2} 30: {1,7,12,6}
Row n = 24 counts the following 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
MAPLE
b:= proc(n) option remember; expand(x*(1 +
add(b(d), d=numtheory[divisors](n) minus {n})))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n)):
seq(T(n), n=1..50); # Alois P. Heinz, Aug 23 2020
MATHEMATICA
chss[n_]:=Prepend[Join@@Table[Prepend[#, n]&/@chss[d], {d, Most[Divisors[n]]}], {n}];
Table[Length[Select[chss[n], Length[#]==k&]], {n, 30}, {k, 1+PrimeOmega[n]}]
CROSSREFS
A008480 gives rows ends.
A067824 gives row sums.
A073093 gives row lengths.
A334996 appears to be the case of chains ending with 1.
A337071 is the sum of row n!.
A000005 counts divisors.
A001055 counts factorizations.
A001222 counts prime factors with multiplicity.
A067824 counts chains of divisors starting with n.
A074206 counts chains of divisors from n to 1.
A122651 counts chains of divisors summing to n.
A167865 counts chains of divisors > 1 summing to n.
A251683 counts chains of divisors from n to 1 by length.
A253249 counts nonempty chains of divisors.
A337256 counts chains of divisors.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Aug 23 2020
STATUS
approved