OFFSET
1,2
COMMENTS
An alternative wording: Number of chains of divisors starting with n and having all adjacent parts x > y^2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
For n > 1, a(n) = 2*A342083(n).
EXAMPLE
The chains for n = 1, 2, 6, 12, 24, 42, 48:
1 2 6 12 24 42 48
2/1 6/1 12/1 24/1 42/1 48/1
6/2 12/2 24/2 42/2 48/2
6/2/1 12/3 24/3 42/3 48/3
12/2/1 24/4 42/6 48/4
12/3/1 24/2/1 42/2/1 48/6
24/3/1 42/3/1 48/2/1
24/4/1 42/6/1 48/3/1
42/6/2 48/4/1
42/6/2/1 48/6/1
48/6/2
48/6/2/1
MATHEMATICA
cem[n_]:=Prepend[Prepend[#, n]&/@Join@@cem/@Most[Divisors[n]], {n}];
Table[Length[Select[cem[n], And@@Thread[Divide@@@Partition[#, 2, 1]>Rest[#]]&]], {n, 30}]
CROSSREFS
The restriction to powers of 2 is A018819.
Not requiring strict inferiority gives A067824.
The weakly inferior version is twice A337135.
The case ending with 1 is counted by A342083.
The strictly superior version is A342084.
The weakly superior version is A342085.
A001055 counts factorizations.
A038548 counts inferior (or superior) divisors.
A056924 counts strictly inferior (or strictly superior) divisors.
A067824 counts strict chains of divisors starting with n.
A074206 counts ordered factorizations.
A167865 counts strict chains of divisors > 1 summing to n.
A253249 counts strict chains of divisors.
A334997 counts chains of divisors of n by length.
KEYWORD
nonn,changed
AUTHOR
Gus Wiseman, Mar 05 2021
STATUS
approved